Cosine_Transform.ipynb

{
 "metadata": {
  "name": "Cosine_Transform"
 },
 "name": "Cosine_Transform",
 "nbformat": 3,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "%load_ext sympyprt",
     "language": "python",
     "outputs": [],
     "prompt_number": 113
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "from sympy import *",
     "language": "python",
     "outputs": [],
     "prompt_number": 114
    },
    {
     "cell_type": "markdown",
     "source": "Examples of cosine transformations. We use the definition\n$$\n\\mathcal{COS}_t \\left[f(t)\\right]\\left(w\\right) := \\frac{\\sqrt{2}}{\\sqrt{\\pi}} \\int_0^{\\infty} f(t) \\cos(t \\cdot w) \\mathrm{d}t\n$$"
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "t = Symbol(\"t\")\nw = Symbol(\"w\")",
     "language": "python",
     "outputs": [],
     "prompt_number": 115
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": "n = Symbol(\"n\", integer=True)",
     "language": "python",
     "outputs": [],
     "prompt_number": 116
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a = Symbol(\"a\")\nb = Symbol(\"b\")",
     "language": "python",
     "outputs": [],
     "prompt_number": 117
    },
    {
     "cell_type": "markdown",
     "source": "The following examples are taken from 'Bronstein', 6th edition, page 1103ff"
    },
    {
     "cell_type": "markdown",
     "source": "1"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Piecewise((1, And(0<=t, t<=a)), (0, t>a))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMUAAAA3BAMAAABOTJPRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZrsQze8yiatUmUQi\n3XZT92bJAAADoElEQVRYCb1XTWgTQRR+u5tum+42SW1BPNQWFdQqNYigvdj0IFXEgiAWxMMevSXW\ni3qoxYOIP20QQShUjUgP/rSh1IO9ZEGR4sVcPOhBtlgEQaSlEimN4nszm2ajSZqJnTzIvLfzzfe+\n+Uv2BQBtEzVy7cBpufkp+5GwdI36jHQJ6BmWr9Eel68xlayBhoUa2s0yQlpirwd9k4vNYhvA0O7c\nEBjbzAZN2QD60Mpa97+BGprwdO50Y/267emFl/yBoYFeFzEisIdC0gAopxFkI2gU2Sp3xi6bB267\ng3uOKv1h9ugLQSsFghr6ImMbnTwLe8BGH2Kb4qLg72NwTxxSFKyroU/dsP3z8zCTXUiC8fijgyQ3\nB0aB+XFsoeFVB7YuSlGnjW00CVEL/boaELTgMtTHzCUV56o6yNEGsOHWBc8pmAN2ZgxlgP4JXcoi\nmco0zCyYWY3tNQqi3blALZqShifkJ1AFjaMUsREiGsoiwJKWJW6UGoDpZ9zXxeADRloHqLTxLgpw\n9zPhuAiUqWwdpPFbWyZa7kVw7hY9wbsk6w7EwYh50FaHQMAzf0DSlZyHmQEzwzVGIM7oMHeNfDSs\npLHDh2EEPxzVFkIYo+HxVHp3LbgIjQ/5Xh1TaGJkbx1s6uzXw+jvY9iMH47ud6cBRgSOYy9bhzn4\n6ynFRU0f7QNlMgHTPxzEx74UDDISLSM2wHbspLX8hcK9rUyO71UBUfzBRopZmjZKuGTbV0V+8+o2\nNKcUc47QLg96yhNLCo1yv7gbpNkU2aBEZdLczl33MmP+E1LpZku2F7ZkAUxvnJSvAamkfJFG9ost\nV8f8KTc/y/6+Bhqj8r8g/D1oWmVWU1CL+hOXygwtAbH3hxpDtJRQQS06A6r4TWQaQeJpj4qzg7Zn\ner2gRDyPlYVMI8rGaoPxYhyvhrYChvhtJ43ZE5M8ea6g+L4lvaZWUIvqq6CL/7lj61h7abU6lFt1\nGvMaBbWokQGUETWmkZ/aOJ1JG5Y6+TxBK1+LVq+RK+mxIO+n3APQ5DmZoJWvRXERKCNqtA6lA7gp\nTMJchZ6w24OOa/BaFM/cX92ZNzh+lvIw/5OlL0Mb72C9uFf5WrSr2rvri7dQtoO7WU6As+bRgBui\nw4I/X4vOgI9OTMxor/yTFpJ09v+Q2LPNh76RZ1ZYi/rPf80BlXvSkG210Lgivr3Cy07FhCnChKa0\nMEWYYNTihd4eEp6XMME4I0wRJ3SLU0QYfwCQnAw+wP5LkgAAAABJRU5ErkJggg==\n",
       "prompt_number": 118,
       "text": "\n\u23a71  for t \u2264 a \u2227 t \u2265 0\n\u23a8                    \n\u23a90      for t > a    "
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# No piecewise :-/",
     "language": "python",
     "outputs": [],
     "prompt_number": 119
    },
    {
     "cell_type": "markdown",
     "source": "4"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73ZnN\n72bDLMX7AAAAqUlEQVQYGWNgAAJGZRAJBixh32FMIE0/Nkfkr81IFlOX+R8BSDHYH6gNpn4ijMHA\nwLIBweZsYGiB8ZwYGKbC2BoMDJ+hbA4FBpYPUDaTA/Oe1QkQThMDAyeICaQZtjAw8DswMDDnFzAw\nTmBg8AcKMXAeYGAFir0EsZm/MEgCKTWGAiC5kiEYSB7nEwCS9Y1A5QzVKUCCgXebAYgCA7afMBYw\ndpFj0QEqDgCk2DEpjB/AOAAAAABJRU5ErkJggg==\n",
       "prompt_number": 120,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\n  ___\n\u2572\u2571 t "
      }
     ],
     "prompt_number": 120
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqBAMAAAC9wk0pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73ZnN\n72bDLMX7AAAAv0lEQVQoFWNgAANGZQgNJVnCvqPwGRgGF58j8tdmNAfSi/sfBXwg11p/iDFw/RNR\nDWLZgMrnbEDlO6FyGTRQ+RwKDH6KDKkMi6HCTA4MAcsZ1jEcg/KbGJgFPzL+YCgG8puAeAsDA9sB\n9gsMDxkYmPMLGBgnMDDwPOBWYHgAlOM8wMDqwMDA78CZwAjiM39hkARSvAayAWxAmoFhJUMwkGRR\ni1DLAPPrG4HakQDvNgMkHtCmnyhcBkb0tOWAJA8A9/I+EPFL9esAAAAASUVORK5CYII=\n",
       "prompt_number": 121,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\n  ___\n\u2572\u2571 w "
      }
     ],
     "prompt_number": 121
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABYAAAAqBAMAAABFIrbeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73ZnN\n72bDLMX7AAAAqUlEQVQYGWNgAAJGZRAJBixh32FMIE0/Nkfkr81IFlOX+R8BSDHYH6gNpn4ijMHA\nwLIBweZsYGiB8ZwYGKbC2BoMDJ+hbA4FBpYPUDaTA/Oe1QkQThMDAyeICaQZtjAw8DswMDDnFzAw\nTmBg8AcKMXAeYGAFir0EsZm/MEgCKTWGAiC5kiEYSB7nEwCS9Y1A5QzVKUCCgXebAYgCA7afMBYw\ndpFj0QEqDgCk2DEpjB/AOAAAAABJRU5ErkJggg==\n",
       "prompt_number": 122,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\n  ___\n\u2572\u2571 t "
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "markdown",
     "source": "7"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(a+t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAmBAMAAAC10Z+jAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAAAqElEQVQoFWNggAEhAxgLQbvmFyA4cBb/EBZsnb8aiz/hXhtwxn9M8GEAHcXhgGy5\nO4TDGYAsWAPh8KMEK1TQHyTHllMFUQIRtH61DcidxrALWRDIZ2DgWcCwG0XwC5DHG8CwHEhxz5z5\nauZMBQYGFlBw9BswfgRSQAAxk2cCkOkvwLOgAEmQKYEdqL2hTyEBSZCv4CADA/Oeg2oNSILs2xzA\nPChhDucAAPxJOGpDLSvQAAAAAElFTkSuQmCC\n",
       "prompt_number": 123,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\na + t"
      }
     ],
     "prompt_number": 123
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAABBCAMAAACJieoTAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n1f8B/fs8/dnQKyEAAAAASUVORK5CYII=\n",
       "prompt_number": 124,
       "text": "\n              \u239b               \u2502  2  2\u239e\n  ___ \u256d\u2500\u256e3, 2 \u239c 1/2, 0        \u2502 a \u22c5w \u239f\n\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u239f\n      \u2570\u2500\u256f2, 4 \u239d1/2, 0, 0  1/2 \u2502   4  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                 2\u22c5\u03c0                  "
      }
     ],
     "prompt_number": 124
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAABBCAMAAACJieoTAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n1f8B/fs8/dnQKyEAAAAASUVORK5CYII=\n",
       "prompt_number": 125,
       "text": "\n              \u239b               \u2502  2  2\u239e\n  ___ \u256d\u2500\u256e3, 2 \u239c 1/2, 0        \u2502 a \u22c5w \u239f\n\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u239f\n      \u2570\u2500\u256f2, 4 \u239d1/2, 0, 0  1/2 \u2502   4  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                 2\u22c5\u03c0                  "
      }
     ],
     "prompt_number": 125
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAmBAMAAAC10Z+jAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAAAqElEQVQoFWNggAEhAxgLQbvmFyA4cBb/EBZsnb8aiz/hXhtwxn9M8GEAHcXhgGy5\nO4TDGYAsWAPh8KMEK1TQHyTHllMFUQIRtH61DcidxrALWRDIZ2DgWcCwG0XwC5DHG8CwHEhxz5z5\nauZMBQYGFlBw9BswfgRSQAAxk2cCkOkvwLOgAEmQKYEdqL2hTyEBSZCv4CADA/Oeg2oNSILs2xzA\nPChhDucAAPxJOGpDLSvQAAAAAElFTkSuQmCC\n",
       "prompt_number": 126,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\na + t"
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "markdown",
     "source": "8"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(a-t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAlBAMAAAAzRe0NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAAAl0lEQVQoFWNggAEhAxgLQbvmFyA4cBb/EBZsnb8aiz/hXhtwxn9M8GEAHcXhgMVy\nzgAsgvzYgtUfpJAtpwpZvfWrbUDuNIZdyIJAPgMDzwKG3SiCX4A83gCG5UCKYyYIJDAwsICCo9+A\n8SOQggOeCUCmvwDPggK4EAMDUwI7UHtDn0ICkiBfwUEGBuY9B9UakATZtzkwAABL0TN8XXmeYAAA\nAABJRU5ErkJggg==\n",
       "prompt_number": 127,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\na - t"
      }
     ],
     "prompt_number": 127
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAARkAAABBCAMAAADSZCALAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nQ9FlPAutAAAAAElFTkSuQmCC\n",
       "prompt_number": 128,
       "text": "\n               \u239b               \u2502  2  2  -2\u22c5\u2148\u22c5\u03c0\u239e\n   ___ \u256d\u2500\u256e3, 2 \u239c 1/2, 0        \u2502 a \u22c5w \u22c5\u212f      \u239f\n-\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n       \u2570\u2500\u256f2, 4 \u239d1/2, 0, 0  1/2 \u2502       4      \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                      2\u22c5\u03c0                      "
      }
     ],
     "prompt_number": 128
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAARkAAABBCAMAAADSZCALAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nQ9FlPAutAAAAAElFTkSuQmCC\n",
       "prompt_number": 129,
       "text": "\n               \u239b               \u2502  2  2  -2\u22c5\u2148\u22c5\u03c0\u239e\n   ___ \u256d\u2500\u256e3, 2 \u239c 1/2, 0        \u2502 a \u22c5w \u22c5\u212f      \u239f\n-\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c               \u2502 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n       \u2570\u2500\u256f2, 4 \u239d1/2, 0, 0  1/2 \u2502       4      \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                      2\u22c5\u03c0                      "
      }
     ],
     "prompt_number": 129
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAlBAMAAAAzRe0NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAAAl0lEQVQoFWNggAEhAxgLQbvmFyA4cBb/EBZsnb8aiz/hXhtwxn9M8GEAHcXhgMVy\nzgAsgvzYgtUfpJAtpwpZvfWrbUDuNIZdyIJAPgMDzwKG3SiCX4A83gCG5UCKYyYIJDAwsICCo9+A\n8SOQggOeCUCmvwDPggK4EAMDUwI7UHtDn0ICkiBfwUEGBuY9B9UakATZtzkwAABL0TN8XXmeYAAA\nAABJRU5ErkJggg==\n",
       "prompt_number": 130,
       "text": "\n  1  \n\u2500\u2500\u2500\u2500\u2500\na - t"
      }
     ],
     "prompt_number": 130
    },
    {
     "cell_type": "markdown",
     "source": "9"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(a**2+t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAmBAMAAACSfx5LAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAABCUlEQVQ4EWNgQAZCBsg8VLZrfgGqAAqPf1SSoXX+ajzhhxJcQ47zHzf4QKlnWNJU\n0I1wS3KACokx+AqgyjImsFyEivgz8KOFOMsHhs9QSRYG+QZknRwODA6MP+AiWyEsdwjFGcDAwA3E\nEMCzAULXQCiQJaehUgwMZgwCYDZU0p+BgTmBESjCllPFwJLY44Akaf1qG4ObxBGgyDSGXQz9//+D\n5RigOqcxcPz//4GBgWcBw26IBIiESn6BivAGMCyHMrlnznw1c6YCAwPQkxDQb8D4EcoEUhCdPBOg\nIv4CPAsK4LIQSaYEdogIb0OfQgKaJF/BQYgI856Dag1okuzbHOAiSAxzJDYDAwAVFVLpFBkgTAAA\nAABJRU5ErkJggg==\n",
       "prompt_number": 131,
       "text": "\n   1   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2    2\na  + t "
      }
     ],
     "prompt_number": 131
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAApBAMAAAAIQeLLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfLrdviLuJn0SMNh/ueapN7Qsv28AAAAASUVORK5CYII=\n",
       "prompt_number": 132,
       "text": "\n  ___   ___                         \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5(-sinh(a\u22c5w) + cosh(a\u22c5w))\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                2\u22c5a                 "
      }
     ],
     "prompt_number": 132
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAApBAMAAAAIQeLLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfLrdviLuJn0SMNh/ueapN7Qsv28AAAAASUVORK5CYII=\n",
       "prompt_number": 133,
       "text": "\n  ___   ___                         \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5(-sinh(a\u22c5w) + cosh(a\u22c5w))\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                2\u22c5a                 "
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAArBAMAAAC0kTKVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRKsZCLTDmMy039xjet8o+V94a5JESltj6QAAAABJRU5ErkJggg==\n",
       "prompt_number": 134,
       "text": "\na\u22c5cos(\u221e\u22c5t)\u22c5sinh(\u221e\u22c5a) - a\u22c5cos(\u221e\u22c5t)\u22c5cosh(\u221e\u22c5a) + a - t\u22c5sin(\u221e\u22c5t)\u22c5sinh(\u221e\u22c5a) + t\u22c5sin\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                           \u239b 2    2\u239e                          \n                                         a\u22c5\u239da  + t \u23a0                          \n\n(\u221e\u22c5t)\u22c5cosh(\u221e\u22c5a)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               \n               "
      }
     ],
     "prompt_number": 134
    },
    {
     "cell_type": "markdown",
     "source": "10"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(a**2-t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAlBAMAAAAU62zlAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEKtEMol2VCK73Zlm\n781XBQ0aAAAA90lEQVQ4EWNgQAZCBsg8VLZrfgGqAAqPf1SSoXX+ajzhhxJcQ47zHzf4QKlnWNJU\n0I1wS3KACokx+AqgyjImsFyEivgz8KOFOMsHhs9QSRYG+QZknRwODA6MP+AiW+EsEIMzgIGBG4gh\ngGcDjAWmQZachouYMQjA2UCGPwMDcwIjkMGWU8XAktjjAGTCgPWrbQxuEkeA3GkMuxj6//+HSYDp\naQwc//9/YGDgWcCwG0UCxPkCFeENYFgOZXLMBIEEBgagJyGg34DxI5QJp3gmQJn+AjwLCuDCEAZT\nAjuEwdvQp5CAJslXcBAiwrznoFoDmiT7NgewCADW8U37ig+kXAAAAABJRU5ErkJggg==\n",
       "prompt_number": 135,
       "text": "\n   1   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2    2\na  - t "
      }
     ],
     "prompt_number": 135
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAApBAMAAADNM3haAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrsQmSKrRHZUzYnd\n72ZiHOLWAAAEDElEQVRYCe1WTYjUZhh+ZrIzk8xk4rCHOfTgjq2H7aESrH9gddZSZA9FguKCpeqU\nRd1L2RR7EPQQLIuLW6ZzUgv9GRFKe2nnoLY3R0FECmVBRMGDKYrsqiz7w+DPwen75ZskX2L2kAb2\ntC9M8j3v9z7Pm/f98mU+gNtAl2y+B1bq9t5KJRLypIYE4FTtlG0LXjbURBwA4kRgbIuIgMBKG8Kc\nV3VW9LKAI0IUpCERLTMOSmyCyCpDu/x+j+dXPet4tDuuoNZwR879QgBFAy7hzikW4LOOYAIDNp/z\nq247DuUS9wOqO+D3vB7EUagddJKUx8rUcB/ZaR5QduPYcwXMf0jHLduB2SgQlqgDHitbwt8oLHGa\nt3BZM6RzLIhTzSCOQGGJdwCPNcLi07xSqnoj7dkOsIacsz81+6/n/jj02CIwT7/J2TbWjmIKtzgm\nV8CU4TqUeh3a90/JzyTk+g9IPdHllmo6mKmwhLvoh6rFrqCqv9i+9TiNqkCuhVFpgaYy1AaJwtNW\nXxut2/gHvwLeG+YQ+eUsDpYuo9A6iazuSGAQn6KgNlQ7b6FIPmLlvmtAqjDCes4aQUo/JBsEDtLs\nLZhYwBqbLshMA8/RN5T7cEnq4DxwkzPEq/QKmzZ3kOmcMnNcQmvjExyv6lVDMaGSLmOlmyiU6C63\n/KqvZJnQ5/QbXyyxpCW8oKRt4AHUBuSmMo1HwHUK2Psu2SA16CjZMeTo4bR54E22u45LFFu4DZzF\nj9B0qJSJsShsI91o/+he1U1nc+ygjmbOdbyk0jQyL1DVkbf7arAj2+smfakfGDcAkjhsSrQ0v2M3\n+xj12gvcwJ8stwXLrTpXKxKBrbpWwl9eUnqRUkt4rlDhaUuipFRR2Ki92L+AzMK/KFiOxICutRuk\nMYid/MVyWD/vqxC1f26m4ladtlWbXPkStBrOsKQmay8uAnczv8gomjtaMr38FfKF7VtoxlVa+CeQ\nTUeiaHxWs3BPekBFod9lFYdpFg+73Ypbtar3UQBkC9rkjF1+/dX4b+XXNm0X4Ou5LRNIjV0Zm6A2\nkOstU8bOQBvegxnaNo5Ebs+jMQPlqZFJA5hzWfKiz+RV97DU9iec0UdBnNeDOAKFJbzPIFsG13jV\nLmJrLVqBtcS3k/5w2VFQgrY9eqySTxGrpm0QLmXUj6Q3uyaiZcZBiS2RLLFqCrBCUttELIcfSZx0\nx0GJb2iVI1hC1S5v9Z6gA/QvtuKW4HFXqasdSNyBZx83EmvEFZCN1Ju4nMTxRQtfJhaJK6C2cC3i\nwx1XJnb8B/zcHZuXhCC95OfuJBqxuekh59wdm5eIMNU7dycSiUlWLImfu2PyEoWfgMzP3YlU4pFT\nG+ZO83N3PF6i6GK3u8jP3f9L5j+7rnrxi77RhQAAAABJRU5ErkJggg==\n",
       "prompt_number": 136,
       "text": "\n  ___   ___                        \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5(sin(a\u22c5w) - \u2148\u22c5cos(a\u22c5w))\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                2\u22c5a                "
      }
     ],
     "prompt_number": 136
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAArBAMAAACXymNAAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAbOhxC/Lf7uF5B+0Ik1F82N5CAAAAABJRU5ErkJggg==\n",
       "prompt_number": 137,
       "text": "\n\u2148\u22c5a\u22c5sin(\u221e\u22c5a)\u22c5cos(\u221e\u22c5t) + a\u22c5cos(\u221e\u22c5a)\u22c5cos(\u221e\u22c5t) - a + t\u22c5sin(\u221e\u22c5a)\u22c5sin(\u221e\u22c5t) - \u2148\u22c5t\u22c5si\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                          \u239b   2    2\u239e                         \n                                        a\u22c5\u239d- a  + t \u23a0                         \n\nn(\u221e\u22c5t)\u22c5cos(\u221e\u22c5a)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               \n               "
      }
     ],
     "prompt_number": 137
    },
    {
     "cell_type": "markdown",
     "source": "11"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b/(b**2+(a-t)**2) + b/(b**2+(a+t)**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAsBAMAAACOKakdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAASUVORK5CYII=\n",
       "prompt_number": 138,
       "text": "\n      b               b      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2          2    2          2\nb  + (a + t)    b  + (a - t) "
      }
     ],
     "prompt_number": 138
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 139
    },
    {
     "cell_type": "markdown",
     "source": "12"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(a+t)/(b**2+(a+t)**2) + (a-t)/(b**2+(a-t)**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAAsBAMAAACOKakdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
       "prompt_number": 140,
       "text": "\n    a - t           a + t    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2          2    2          2\nb  + (a - t)    b  + (a + t) "
      }
     ],
     "prompt_number": 140
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 141
    },
    {
     "cell_type": "markdown",
     "source": "13"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(a**2+t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAqBAMAAAD8NjCWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
       "prompt_number": 142,
       "text": "\n     1      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   _________\n  \u2571  2    2 \n\u2572\u2571  a  + t  "
      }
     ],
     "prompt_number": 142
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAABGCAMAAABVC5AHAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nUPo0Fy+if/4y9TnCfwD+uzgAGSpcFwAAAABJRU5ErkJggg==\n",
       "prompt_number": 143,
       "text": "\n              \u239b          \u2502  2  2\u239e\n  ___ \u256d\u2500\u256e2, 1 \u239c1/2       \u2502 a \u22c5w \u239f\n\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c          \u2502 \u2500\u2500\u2500\u2500\u2500\u239f\n      \u2570\u2500\u256f1, 3 \u239d0, 0  1/2 \u2502   4  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                 ___             \n             2\u22c5\u2572\u2571 \u03c0              "
      }
     ],
     "prompt_number": 143
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAABGCAMAAABVC5AHAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nUPo0Fy+if/4y9TnCfwD+uzgAGSpcFwAAAABJRU5ErkJggg==\n",
       "prompt_number": 144,
       "text": "\n              \u239b          \u2502  2  2\u239e\n  ___ \u256d\u2500\u256e2, 1 \u239c1/2       \u2502 a \u22c5w \u239f\n\u2572\u2571 2 \u22c5\u2502\u2576\u2510     \u239c          \u2502 \u2500\u2500\u2500\u2500\u2500\u239f\n      \u2570\u2500\u256f1, 3 \u239d0, 0  1/2 \u2502   4  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                 ___             \n             2\u22c5\u2572\u2571 \u03c0              "
      }
     ],
     "prompt_number": 144
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEsAAAA4BAMAAABH1hi2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3mR6HN4TvgCinJxkHUOB6QAAAABJRU5ErkJggg==\n",
       "prompt_number": 145,
       "text": "\n       1        \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n        ________\n       \u2571  2     \n      \u2571  a      \nt\u22c5   \u2571   \u2500\u2500 + 1 \n    \u2571     2     \n  \u2572\u2571     t      "
      }
     ],
     "prompt_number": 145
    },
    {
     "cell_type": "markdown",
     "source": "15"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t**(-a)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAANBAMAAABFt2PeAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIjK7iUSZzd12ZqtUECkr\naBAAAABhSURBVAgdY2CAg5mTBRgYGBUgfLYJ94AMZgeGZWlpaQvkLqgDeXwBELkTDFOADD0IhyGa\noXUBQ1hFJoTLtmraAQYGS6gchHqEzGN6gMzjMkDmcU/gQeKyH1iLxOPJVEDwANicEi6XoYpaAAAA\nAElFTkSuQmCC\n",
       "prompt_number": 146,
       "text": "\n -a\nt  "
      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAL0AAAA2BAMAAABgjoUYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 147,
       "text": "\n -a + 1/2  a - 1  \u239b  a   1\u239e\n2        \u22c5w     \u22c5\u0393\u239c- \u2500 + \u2500\u239f\n                  \u239d  2   2\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n             \u239ba\u239e           \n            \u0393\u239c\u2500\u239f           \n             \u239d2\u23a0           "
      }
     ],
     "prompt_number": 147
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAANBAMAAABFt2PeAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIjK7iUSZzd12ZqtUECkr\naBAAAABhSURBVAgdY2CAg5mTBRgYGBUgfLYJ94AMZgeGZWlpaQvkLqgDeXwBELkTDFOADD0IhyGa\noXUBQ1hFJoTLtmraAQYGS6gchHqEzGN6gMzjMkDmcU/gQeKyH1iLxOPJVEDwANicEi6XoYpaAAAA\nAElFTkSuQmCC\n",
       "prompt_number": 148,
       "text": "\n -a\nt  "
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "markdown",
     "source": "16"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAAQBAMAAAAc1rnfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVDLN\n3atI+RUPAAAAfElEQVQYGWNgQAGzUXhAjiG6wBVkASalkLaiBiQRI84PXA8gfEZjY2NDlp/cB5gF\nkBRwXWBK4N0wASHC8YC3kZ9jAwMDo6IJRNRQyIpZCsgMY3BCKAOy2AoYUlAE+AMVHVAE/BtQuAwM\n8x0YOFGEWBcwSKAIcBoKOSALAAAJHxM1XFAJqAAAAABJRU5ErkJggg==\n",
       "prompt_number": 149,
       "text": "\n -a\u22c5t\n\u212f    "
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAAtBAMAAABfZVhzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n31i2AAAAAElFTkSuQmCC\n",
       "prompt_number": 150,
       "text": "\n      ___      \n    \u2572\u2571 2 \u22c5a    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  ___ \u239b 2    2\u239e\n\u2572\u2571 \u03c0 \u22c5\u239da  + w \u23a0"
      }
     ],
     "prompt_number": 150
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAAASBAMAAAA03yjuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 151,
       "text": "-sinh(a\u22c5t) + cosh(a\u22c5t)"
      }
     ],
     "prompt_number": 151
    },
    {
     "cell_type": "markdown",
     "source": "17"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(exp(-b*t)-exp(-a*t))/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFcAAAApBAMAAACyzqjuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVKsy\n3c2S+EuhAAABMUlEQVQ4EWNggIPlDgycB+A8DMYcFJHpDAzMAigiKBxDFN5qBgZeBxQRFM4VFJ6p\n8Il0DRQROIdJKaStqAHOBTJucAQADccKjDg/cG2AyjAaGxsbchZwPUB1F0gWLMXyk+cBqnc4NjAn\n3OHEajDXBaYE3gMTkOR4Nsyd8KEHSQDB5NjA28jPcQAowKhoAhE2MmEwXABhQkm4lKGQFbMUSDCM\nwQlFBRIHQ4qtgCEFSR6ZiSnFH6jogKyCgYElFAQUGBgwpfwbUJUi8TCl5gOTD5ICZCamFOsCBglk\nFUhsTClOQyEHJAXITDxSyMpG2cSEwH/iwQdizBuGalgOkOAp1gQSFPM3kKD4PAlqm98akaA6iAS1\nDH9IUMxDSpJhDCDBZG4FLuJV8y2QJF4xl9EBrIoBHpFetWC4JnwAAAAASUVORK5CYII=\n",
       "prompt_number": 152,
       "text": "\n -b\u22c5t    -a\u22c5t\n\u212f     - \u212f    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      t      "
      }
     ],
     "prompt_number": 152
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAS0AAAAuBAMAAACPLlLHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 153,
       "text": "\n                 \u239b -a\u22c5t      \u239e                  \u239b -b\u22c5t      \u239e\n                 \u239c\u212f          \u239f                  \u239c\u212f          \u239f\n- CosineTransform\u239c\u2500\u2500\u2500\u2500\u2500, t, w\u239f + CosineTransform\u239c\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n                 \u239d  t        \u23a0                  \u239d  t        \u23a0"
      }
     ],
     "prompt_number": 153
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 154
    },
    {
     "cell_type": "markdown",
     "source": "18"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sqrt(t)*exp(-a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADQAAAATBAMAAAAt/zNWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrsQmSKrRHZUzYnd\n72ZiHOLWAAABA0lEQVQoFWNgAAPG////f4Aw0UkmA3QRZgGoiAi6DAPLA6iQKoYUTwBEiDEBVaqj\nKXxvO0SILYCBFWY2UISlwZ5hGlRxGAMD0wYw+4mLi8uDeAMpBj+oVCIDA38BlA2k5jB0MxxkBvNZ\nExgY5BEyDGUMxx98KGQACbMIMJSs8WBgePEE4iyWdy0T/CYwVPxkYDAC6tAAWcfagKSXgUGLgWEj\nUOAjA8NeBm6ILph8vQCzAgMD4wcGhk8vnsIEITSPAjfQcXwKDKzfUSUYGDi/gqxia+Bk/srAYIAq\newUUJFwTHjNoMvAB9SODfgUgj9NDgMHkXSuyOJBtPwFNAMFlRDBRWAATlzK6lSBrXQAAAABJRU5E\nrkJggg==\n",
       "prompt_number": 155,
       "text": "\n  ___  -a\u22c5t\n\u2572\u2571 t \u22c5\u212f    "
      }
     ],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAABDBAMAAAB5Imr9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
       "prompt_number": 156,
       "text": "\n         \u239b      \u239bw\u239e\u239e\n         \u239c3\u22c5atan\u239c\u2500\u239f\u239f\n  ___    \u239c      \u239da\u23a0\u239f\n\u2572\u2571 2 \u22c5cos\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n         \u239d    2    \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                3/4 \n        \u239b     2\u239e    \n    3/2 \u239c    w \u239f    \n 2\u22c5a   \u22c5\u239c1 + \u2500\u2500\u239f    \n        \u239c     2\u239f    \n        \u239d    a \u23a0    "
      }
     ],
     "prompt_number": 156
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAABDBAMAAAB5Imr9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrsQmSKrRHZUzYnd\n72ZiHOLWAAAFs0lEQVRYCc1XX2hbVRj/bm6TmzTJTfCh7kFprFM3n8Jwuj1o4/xXUUpEFDeYDcJ0\n1YeF4cs2nRfZujq1y3RKC0Lrg84nCTJmH0TqREQEyRgyn1yGWkqdJVVqN5HV33fOPTc3ybnJhDzs\ng/v9+f2+891z7rn33HOIpPSvQWpuUDfhNO2bT9fjJu8JN74H1iz6yFt9vs99muisVfEBDW644IbR\nEpw36pyRq/t+D3fJWzU/4vdDWRVxb+oRhfKKaLBRB2FPtQHzBeNE0YeMwq9EfUCNgkf1kX1qoxd5\nTgK3N057ffBw1/ma6N3RuIMnkuDufOPxu+gw9Ve9UDnvsGOdU+FvypE2loE911uMopNluG9KmAjP\n9CeKVFTo2ZeIYhW6quJdypE2ghpWJkXvwXDbVxUdSdP3FP9LhZ79FmMtm8tubK94hHASRdwtt5Mc\nvCXcdjDr8hg9ZgZ3iA1NUGxiguypRYa4/eR8Cfq+hQfoxN/Dwu5fWRpiNpWHGl4YZ3MeV7IIxaXu\nx0WDDtFR2pk+RfHyAYpk8Qzq/d1Gi2SiurCXaQSsVNwS8gOuRBWjPlYiM4OA1qPPV+iuzSsUXnml\naAExaowLOYjGXI4tHmYqDbTf5dh8gqvXgQrNUJxJnhwLj8lGjauRtVsAcbmU/PjMhWN5LseWlilV\nBM3l+Nvkj9MrhxKbgNMkZb1yl7Pb9+QbBnspPYhyBrFV5cSIuSnkO1yJEntn6HNoy8EMYbD01DKF\nly9S3EFXeCrWjaWhr9DIdnMlKqwqh8KeeFNB009mgN6wtADzFtn509STm6doESCSTMfAa2yu0vQz\ndD4u7aocrJhJZLHwjcVMU3KIW15YW8vgRdl9hOyhYVrAywLZIJ7fKrz3J9aN0t4jwvb9c3zPp8BC\nDpQUowJ7s/Cjf7pYq5kHlBZDbuUwaQWg0fHboIXL2RgIHliA3Mt4TzmANblLQ2YNujcN9aHMY1cv\nPSXgWH8C5FGefGMG7E24jDmo9pLhKTeDckJ42HP8vorPqie4W6rAAbwomy+qqNlaZbIKiYO4JZdE\nbieJpcO6P5JqdpyXAAx5CwDTUej1a8U33C1Vu97GGZvs6hQkqNLVEYZnulpuMd/VcoS9QPdkK23s\nXjGil+mrbpazf3c6lZsaVxm8UgTItX/yc0m3RKgUUItheU/5m22TBmqHSz8WkBY7VMWfR94rBre9\n2B9J3poJyNtCP2KBww8TsskRpp1KZAXLOy6t9NEdwOWfa8nRptRBs+SO42gda/RM4p4l81DWs04j\n1xJZuURagLxT0Eu8Cjyeg9pqO9BtZWlW0MEnAJrihHANanKMx30tEslosg7l++ycVbqRqZ9ZicMC\nO03iHQV4S8dcwoEyX2DXk9jdpdlwYWRN7EsfZnj/SY9scFqOArzhMmbdLYdRksnJ7Ens3KRccq3W\n1I8Ck8MiYVpot5x6W/dSLYbbCHnNtVrjHQVMR7wC9LZIayp3IlyJquaDaeVpLY4C0YkPcLgKFZn/\nQiQ1letZGj+sGqfcB6DiJoujwAZ6nCibzDLzoqCbyvmbpKr+qMVfT/YcPQj4S0ENCN2mXNIRGQEK\nW6tkmffgMTmIj+vltg3ceWbgdsT8EgmpIUiUAyoJGEeBkSKfrvYZRQa4Oe/ZhaiZ5UAsKLBte8dH\ngf6sPVfCHizLrZ5jpSsnFxR0tSoy9IqPAsn8joKj6MByckHBKa6kUjX2Ao4C1vAvu/OK4xcl/Nm/\nj4jYP1gSCwrOeOKZqPROVn4VbpalesI7/ykJ9mc7lfDzI14//Sh2/u6CQn/48Y5+UnXIn8k7f3dB\noef9REc/ktOkuDt/wYj1TpOjh6w5DS53/oLwHcY1ia3Q2VbI3fkLIprR8cHYWDDFjP8A2j5TsnLZ\nC8x8PZDRE3ZGj7sodgL/T0bbpUeq7Vgd16t9kd3MDk9WU88saEAXCuc03H+J3sE2zukl2AAAAABJ\nRU5ErkJggg==\n",
       "prompt_number": 157,
       "text": "\n         \u239b      \u239bw\u239e\u239e\n         \u239c3\u22c5atan\u239c\u2500\u239f\u239f\n  ___    \u239c      \u239da\u23a0\u239f\n\u2572\u2571 2 \u22c5cos\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n         \u239d    2    \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                3/4 \n        \u239b     2\u239e    \n    3/2 \u239c    w \u239f    \n 2\u22c5a   \u22c5\u239c1 + \u2500\u2500\u239f    \n        \u239c     2\u239f    \n        \u239d    a \u23a0    "
      }
     ],
     "prompt_number": 157
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 158
    },
    {
     "cell_type": "markdown",
     "source": "19"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t)/sqrt(t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAuBAMAAABUnG2JAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVDLN\n3atI+RUPAAABEElEQVQoFWNgQAGzUXggjiGGyBUUESalkLaiBmQhI84PXA+gAozGxsaGLD+5DzAL\nICvhusCUwLthApIQxwPeRn6ODUARRkUTiLihkBWzFIgZxuAEEYGRbAUMKTA2hOYPVHRAFfFvQOUz\nMMx3YOBEFWNdwCCBKsJpKOSAKjKwvP9o4APFztkPNBHVkEhULgMDtwG6CKsDusg+BgZvVLEnoIhC\nBiwPGBh+IAsw8G1g4Eb1gR8Dh81lBZgiPyDDmoGBFS7Aob+AgTOAgYF/A0wJA+sBBjYgbz9cgIHj\nN8NUIE8UIcJwlSEDyHvEsAAutt4TaAzDKcYJcBF2owYge7E2XICB6SuCDWFx/kIXYUC4hAEALihA\nHkubtrEAAAAASUVORK5CYII=\n",
       "prompt_number": 159,
       "text": "\n -a\u22c5t\n\u212f    \n\u2500\u2500\u2500\u2500\u2500\n  ___\n\u2572\u2571 t "
      }
     ],
     "prompt_number": 159
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAAA9BAMAAABICgZMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nIMfU7+cgGqHNM9ym/Wvll3+G8DeDOaO0K0RPrgAAAABJRU5ErkJggg==\n",
       "prompt_number": 160,
       "text": "\n          \u239b    \u239bw\u239e\u239e \n          \u239catan\u239c\u2500\u239f\u239f \n   ___    \u239c    \u239da\u23a0\u239f \n \u2572\u2571 2 \u22c5cos\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f \n          \u239d   2   \u23a0 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n            ________\n           \u2571      2 \n  ___     \u2571      w  \n\u2572\u2571 a \u22c5   \u2571   1 + \u2500\u2500 \n      4 \u2571         2 \n      \u2572\u2571         a  "
      }
     ],
     "prompt_number": 160
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 161
    },
    {
     "cell_type": "markdown",
     "source": "20"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t**n*exp(-a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAC8AAAAQBAMAAAB0JTvnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIjK7iUSZzd12ZqtU\nEO//KStoAAAAyUlEQVQYGWNgwAouYRUFCmbhkmgES/DOlpqCpIJzpmHIywAGBkYFHo4J/EgSmbwf\neDYA+cwODPcZNMASXGlpaVmMf5kK2BYA+fwBDIcZXMASYIKngdOBQ+ECA4M+A0MmQ9EEuAzrBo4o\nflYFhrCKTIaNDJ4BDFyzEiGSWStz2NYAmZZQtSYMknBdYMYnCJflAYMjigTTBwiX32qWAIoElwGE\nKx+AIszAwD2BByxyX4CBF0WK/cBaMJ/5AMNSFAmeTAUwnzdrJYodAIJoJK5Kdl4EAAAAAElFTkSu\nQmCC\n",
       "prompt_number": 162,
       "text": "\n n  -a\u22c5t\nt \u22c5\u212f    "
      }
     ],
     "prompt_number": 162
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAe8AAABBBAMAAAAKxjHUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nHOrfM6tvAcG5I2vyhjiFAAAAAElFTkSuQmCC\n",
       "prompt_number": 163,
       "text": "\n                        n   1                                  \n                      - \u2500 - \u2500                                  \n                        2   2                                  \n              \u239b     2\u239e                                         \n  ___  -n - 1 \u239c    w \u239f           \u239b      \u239bw\u239e       \u239bw\u239e\u239e         \n\u2572\u2571 2 \u22c5a      \u22c5\u239c1 + \u2500\u2500\u239f       \u22c5cos\u239cn\u22c5atan\u239c\u2500\u239f + atan\u239c\u2500\u239f\u239f\u22c5\u0393(n + 1)\n              \u239c     2\u239f           \u239d      \u239da\u23a0       \u239da\u23a0\u23a0         \n              \u239d    a \u23a0                                         \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                               ___                             \n                             \u2572\u2571 \u03c0                              "
      }
     ],
     "prompt_number": 163
    },
    {
     "cell_type": "markdown",
     "source": "21"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t**(n-1)*exp(-a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEEAAAAQBAMAAAC7Cw8kAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIjK7iUSZzd12ZqtU\nEO//KStoAAAA60lEQVQoFWNgQAWGqFyGS2h8hiMP0USy0PgMDOgqGsEqeGdLTYEpRVbBOdMw5GUA\nAwOjAg/HBH5sKjJ5P/BsAEowOzDcZ9Bg4EpLSwNaCjEDzGH8y1TAtgCogj+A4TCDCxYzeBo4HTgU\nLjAw6DMwZDIUTYAqQXIH6waOKH5WBYawikyGjQyeQAeBQOTvBQxcsxIhnKyVOWxrgExLCBdBmjBI\nIjgg1idULgPLAwZHFCGmDyhcoMutZgmgCHEZoHAZGOShToILc0/ggbPBjPsCDLwoIuwH1qLwGZgP\nMCxFEeHJVEDhM/BmrURxBwAyei9km78UZQAAAABJRU5ErkJggg==\n",
       "prompt_number": 164,
       "text": "\n n - 1  -a\u22c5t\nt     \u22c5\u212f    "
      }
     ],
     "prompt_number": 164
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAU0AAABBBAMAAACna+s4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 165,
       "text": "\n                  -n                    \n                  \u2500\u2500                    \n                  2                     \n          \u239b     2\u239e                      \n  ___  -n \u239c    w \u239f      \u239b      \u239bw\u239e\u239e     \n\u2572\u2571 2 \u22c5a  \u22c5\u239c1 + \u2500\u2500\u239f  \u22c5cos\u239cn\u22c5atan\u239c\u2500\u239f\u239f\u22c5\u0393(n)\n          \u239c     2\u239f      \u239d      \u239da\u23a0\u23a0     \n          \u239d    a \u23a0                      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                   ___                  \n                 \u2572\u2571 \u03c0                   "
      }
     ],
     "prompt_number": 165
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 166
    },
    {
     "cell_type": "markdown",
     "source": "22"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/t*(S(1)/2-1/t+1/(exp(t)-1))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAArBAMAAACTAFvgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfAPHWYr/mGkhIAAAAABJRU5ErkJggg==\n",
       "prompt_number": 167,
       "text": "\n1     1      1\n\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\n2    t       t\n    \u212f  - 1    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      t       "
      }
     ],
     "prompt_number": 167
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 168
    },
    {
     "cell_type": "markdown",
     "source": "23"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACUAAAAUBAMAAAD4luk4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVDLN\n3atI+RUPAAAApElEQVQYGWNgQAOLDNEEGBg4Fdgd0AW5H7A2oIsxTGCfgCY2m4EhEU2IwZCBawG6\n2BWGLu4GJEEmpZC2opb//5HNM+L8wPUArobR2NjYkOUn9wFmAbgYmMF1gSmBdwOyRgYGjge8jfwc\nG8DyjIomEA2GQlbMUhBmGIMThIEg2QoYUhA8CIs/UNEBXcy/AV2EgWG+AwMnuijrAgYJdDFOQyEH\nNDEAD2kbwVmPjzMAAAAASUVORK5CYII=\n",
       "prompt_number": 169,
       "text": "\n     2\n -a\u22c5t \n\u212f     "
      }
     ],
     "prompt_number": 169
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEEAAAA2BAMAAABq/ukPAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 170,
       "text": "\n         2\n       -w \n       \u2500\u2500\u2500\n  ___  4\u22c5a\n\u2572\u2571 2 \u22c5\u212f   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     ___  \n 2\u22c5\u2572\u2571 a   "
      }
     ],
     "prompt_number": 170
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACUAAAAUBAMAAAD4luk4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVDLN\n3atI+RUPAAAApElEQVQYGWNgQAOLDNEEGBg4Fdgd0AW5H7A2oIsxTGCfgCY2m4EhEU2IwZCBawG6\n2BWGLu4GJEEmpZC2opb//5HNM+L8wPUArobR2NjYkOUn9wFmAbgYmMF1gSmBdwOyRgYGjge8jfwc\nG8DyjIomEA2GQlbMUhBmGIMThIEg2QoYUhA8CIs/UNEBXcy/AV2EgWG+AwMnuijrAgYJdDFOQyEH\nNDEAD2kbwVmPjzMAAAAASUVORK5CYII=\n",
       "prompt_number": 171,
       "text": "\n     2\n -a\u22c5t \n\u212f     "
      }
     ],
     "prompt_number": 171
    },
    {
     "cell_type": "markdown",
     "source": "24"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t**(-S(1)/2)*exp(-a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAAvBAMAAADp+gynAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVKsy\nzd3FjUmUAAABE0lEQVQoFWNgQIBp0gcQHBArhHUCigDLBV4UPgPPhtMNqCKG0gKoAggeo7GxsSED\n/////xFi2Fk7wcKMiiYw6QdgRhiDE1TA+RKIwVbAkAIV4FIAMfgDFR1ANBAwHwCR/g0gEgx4uUDU\nfAcGTgifgU0CxGBdwACmQWww4DQUcoAyB5QCBhMy+ECRY3iARqGYgBaxDAyH0c0PQRPg2cDAcgBZ\njNuBgTUBWcAbGAENyAJ7GBjOI/NZNjA03zOCigA54EgKgqlo+sXAMBXI+QMTYIhlYMhhYOBBOLz/\nAGcAAwMjEEMBXwBbAwMDtwI4bkFiXF9ARvAukARxwKBYA0hxGR2A8ICkPkI7RGz+ArgchMGD4AMA\nu78+mEfwWpUAAAAASUVORK5CYII=\n",
       "prompt_number": 172,
       "text": "\n  -a \n  \u2500\u2500 \n  t  \n \u212f   \n\u2500\u2500\u2500\u2500\u2500\n  ___\n\u2572\u2571 t "
      }
     ],
     "prompt_number": 172
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 173,
       "text": "\n         \u239b                         \u239b               \u2148\u22c5\u03c0\u239e                       \n         \u239c                         \u239c               \u2500\u2500\u2500\u239f                       \n     7/8 \u239c      ___ 4 ___ 4 ___    \u239c    ___   ___   4 \u239f            4 ____ 4 __\n-(-1)   \u22c5\u239d- 2\u22c5\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u0393(3/4) + 2\u22c5\u2572\u2571 -1 \u22c5\u2572\u2571 a\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n                                                                              \n\n           \u239b               \u2148\u22c5\u03c0\u239e                                  \u239b            \n           \u239c               \u2500\u2500\u2500\u239f                                  \u239c            \n_ 4 ___    \u239c    ___   ___   4 \u239f              ___ 4 ___ 4 ___     \u239c    ___   __\n \u22c5\u2572\u2571 w \u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u0393(3/4) - 2\u22c5\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                            __\n                                                                     ___   \u2571  \n                                                                 4\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\n\n   \u2148\u22c5\u03c0\u239e                                   \u239b               \u2148\u22c5\u03c0\u239e                \n   \u2500\u2500\u2500\u239f                                   \u239c               \u2500\u2500\u2500\u239f                \n_   4 \u239f            4 ____ 4 ___ 4 ___     \u239c    ___   ___   4 \u239f          8 ____\n \u22c5\u212f   \u23a0\u22c5\u0393(3/4) + 2\u22c5\u2572\u2571 -1 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u0393(3/4) - \u2572\u2571 -1 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n___________                                                                   \n ___   ___                                                                    \n\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)                                                            \n\n                                                                  \u2148\u22c5\u03c0        \u239e\n    _____________                                                 \u2500\u2500\u2500        \u239f\n   \u2571   ___   ___     \u239b  ___   ___   ___\u239e     \u239b  ___   ___   ___\u239e   8         \u239f\n\u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5sin\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5sinh\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f   \u22c5\u0393(-1/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n                                                                              \n\n  -\u2148\u22c5\u03c0\n  \u2500\u2500\u2500\u2500\n   8  \n\u22c5\u212f    \n\u2500\u2500\u2500\u2500\u2500\u2500\n      \n      \n      "
      }
     ],
     "prompt_number": 173
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 174,
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\u2572\u2571\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n______                                                                        \n  ___                                                                         \n\u2572\u2571 w  \u22c5\u0393(3/4)                                                                 \n\n                                                               \u2148\u22c5\u03c0        \n _____________                                                 \u2500\u2500\u2500        \n\u2571   ___   ___     \u239b  ___   ___   ___\u239e     \u239b  ___   ___   ___\u239e   8         \n  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5sin\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5sinh\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f   \u22c5\u0393(-1/4)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                          \n                                                                          \n                                                                          "
      }
     ],
     "prompt_number": 174
    },
    {
     "cell_type": "markdown",
     "source": "25"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t**(-S(3)/2)*exp(-a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAAuBAMAAAAipt8CAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVKsy\nzd3FjUmUAAABB0lEQVQoFWNgQIBp0gcQHBArhHUCigDLBV4UPgPPhtMNqCKG0gKoAggeo7GxsSED\n/////xFi2Fk7wcKMiiYw6QdgRhiDE1TA+RKIwVbAkAIV4FIAMfgDFR1ANBAwHwCR/g0gEgx4uUDU\nfAcGTgifgU0CxGBdwACmQWww4DQUcoAyB5QCBhMy+IDbMauU0OQesKMJMPiiCTBeQRNg4EONac4F\nrAtQlHAY8B1AEWAQTELm+yBzQOww9Jj+wcCwyBBJFc8HBk4Fdge4CIftYwWeDawNcAEGVgUGhgns\nSA7jPwCUTEQoYDgPZHMtQBIQBbK7eBoQIpsYFrD8/49kxi1GJA5I3WIdhGoA6Tk9lrjPvSEAAAAA\nSUVORK5CYII=\n",
       "prompt_number": 175,
       "text": "\n -a \n \u2500\u2500 \n t  \n\u212f   \n\u2500\u2500\u2500\u2500\n 3/2\nt   "
      }
     ],
     "prompt_number": 175
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 176,
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                                5/4  5/4          \n  ___ \u239c            \u239d                                     8\u22c5a   \u22c5w             \n\u2572\u2571 w \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      \u239c                                                                       \n      \u239d                                                                       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___ \u239c       \u239c         ___   ___   4 \u239f       \n\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f         9\u22c5\u2572\u2571 \u03c0 \u22c5\u239dbesseli\u239d3/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 - bess\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                       7/4  7/\n                                                                   16\u22c5a   \u22c5w  \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                        4\u22c5\u0393(5/4)                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n   \u239b                    \u2148\u22c5\u03c0\u239e\u239e  -7\u22c5\u2148\u22c5\u03c0\u239e                                        \n   \u239c                    \u2500\u2500\u2500\u239f\u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u239f                                        \n   \u239c         ___   ___   4 \u239f\u239f    8   \u239f                                        \nelj\u239d3/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f      \u239f           \u239b       \u239b                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u0393(-3/4)   \u239c       \u239c                    \n4                                    \u239f           \u239c       \u239c          ___   ___ \n                                     \u23a0           \u239dbesseli\u239d-1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                   ___                                        \n                                 \u2572\u2571 \u03c0                                         \n\n                                                                              \n                                                                  \u239b       \u239b   \n                                                                  \u239c       \u239c   \n \u2148\u22c5\u03c0\u239e          \u239b                     \u2148\u22c5\u03c0\u239e\u239e  \u2148\u22c5\u03c0                   \u239c       \u239c   \n \u2500\u2500\u2500\u239f          \u239c                     \u2500\u2500\u2500\u239f\u239f  \u2500\u2500\u2500                   \u239cbesseli\u239d1/2\n  4 \u239f          \u239c          ___   ___   4 \u239f\u239f   8                  \u03c0\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n\u212f   \u23a0 + besselj\u239d-1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f   \u22c5\u0393(1/4)\u22c5\u0393(3/4)     \u239d           \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n           4 ___ 4 ___                                                        \n         2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w                                                         \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n                                                                       \u239e\n                 \u2148\u22c5\u03c0\u239e          \u239b                    \u2148\u22c5\u03c0\u239e\u239e              \u239f\n                 \u2500\u2500\u2500\u239f          \u239c                    \u2500\u2500\u2500\u239f\u239f  -\u2148\u22c5\u03c0        \u239f\n      ___   ___   4 \u239f          \u239c         ___   ___   4 \u239f\u239f  \u2500\u2500\u2500\u2500        \u239f\n, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0   besselj\u239d1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u239f   8          \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f    \u22c5\u0393(-1/4)\u239f\n    4                                  4                \u23a0              \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                     4 ___ 4 ___                                       \u239f\n                   2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u0393(3/4)                                \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                        \n                                                                        "
      }
     ],
     "prompt_number": 176
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 177,
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                                5/4  5/4          \n  ___ \u239c            \u239d                                     8\u22c5a   \u22c5w             \n\u2572\u2571 w \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      \u239c                                                                       \n      \u239d                                                                       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___ \u239c       \u239c         ___   ___   4 \u239f       \n\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f         9\u22c5\u2572\u2571 \u03c0 \u22c5\u239dbesseli\u239d3/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 - bess\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                       7/4  7/\n                                                                   16\u22c5a   \u22c5w  \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                        4\u22c5\u0393(5/4)                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n   \u239b                    \u2148\u22c5\u03c0\u239e\u239e  -7\u22c5\u2148\u22c5\u03c0\u239e                                        \n   \u239c                    \u2500\u2500\u2500\u239f\u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u239f                                        \n   \u239c         ___   ___   4 \u239f\u239f    8   \u239f                                        \nelj\u239d3/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f      \u239f           \u239b       \u239b                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u0393(-3/4)   \u239c       \u239c                    \n4                                    \u239f           \u239c       \u239c          ___   ___ \n                                     \u23a0           \u239dbesseli\u239d-1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                   ___                                        \n                                 \u2572\u2571 \u03c0                                         \n\n                                                                              \n                                                                  \u239b       \u239b   \n                                                                  \u239c       \u239c   \n \u2148\u22c5\u03c0\u239e          \u239b                     \u2148\u22c5\u03c0\u239e\u239e  \u2148\u22c5\u03c0                   \u239c       \u239c   \n \u2500\u2500\u2500\u239f          \u239c                     \u2500\u2500\u2500\u239f\u239f  \u2500\u2500\u2500                   \u239cbesseli\u239d1/2\n  4 \u239f          \u239c          ___   ___   4 \u239f\u239f   8                  \u03c0\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n\u212f   \u23a0 + besselj\u239d-1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\u22c5\u212f   \u22c5\u0393(1/4)\u22c5\u0393(3/4)     \u239d           \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n           4 ___ 4 ___                                                        \n         2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w                                                         \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n                                                                       \u239e\n                 \u2148\u22c5\u03c0\u239e          \u239b                    \u2148\u22c5\u03c0\u239e\u239e              \u239f\n                 \u2500\u2500\u2500\u239f          \u239c                    \u2500\u2500\u2500\u239f\u239f  -\u2148\u22c5\u03c0        \u239f\n      ___   ___   4 \u239f          \u239c         ___   ___   4 \u239f\u239f  \u2500\u2500\u2500\u2500        \u239f\n, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0   besselj\u239d1/2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u239f   8          \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f    \u22c5\u0393(-1/4)\u239f\n    4                                  4                \u23a0              \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                     4 ___ 4 ___                                       \u239f\n                   2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u0393(3/4)                                \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                        \n                                                                        "
      }
     ],
     "prompt_number": 177
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "besselsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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PmfeXR8zEBLrVNtqX9l7V28tnOc4nn6rLl5nr95m7eNr7zD+luGodDPmYe7Wj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\nQMBJ4On4bnfeYF6w+4MqHl/tCsXikwj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       "prompt_number": 178,
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 _____________                   __\n      \u239c            \u239c        \u239c        ___   \u2571   ___   ___             ___   \u2571  \n      \u239c    ___     \u239c        \u239d      \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w            \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\n      \u239c  \u2572\u2571 \u03c0 \u22c5a\u22c5w\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      \u239c            \u239c                                                          \n  ___ \u239c            \u239d                                                          \n\u2572\u2571 w \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      \u239c                                                                       \n      \u239d                                                                       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\u2500\u2500\n___   4 \u239f   8          \u239c    ___   ___   4 \u239f    8            \u239c    ___   ___   4\n w \u22c5\u212f   \u23a0\u22c5\u212f       3\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f         3\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f  \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n___________                                 3/2                               \n ___   ___                 ___ \u239b  ___   ___\u239e                   ___ \u239b  ___   __\n\u2571 a \u22c5\u2572\u2571 w              2\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0               2\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                     5/4  5/4                 \n                                                  8\u22c5a   \u22c5w                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n\u03c0\u239e  -3\u22c5\u2148\u22c5\u03c0        \u239b               \u2148\u22c5\u03c0\u239e  -5\u22c5\u2148\u22c5\u03c0         \u239b               \u2148\u22c5\u03c0\u239e  -\n\u2500\u239f  \u2500\u2500\u2500\u2500\u2500\u2500        \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500\u2500\u2500         \u239c               \u2500\u2500\u2500\u239f  \u2500\n \u239f    8           \u239c    ___   ___   4 \u239f    8            \u239c    ___   ___   4 \u239f   \n \u23a0\u22c5\u212f         3\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f         3\u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  3/2                                  5/2                                 5/2\n_\u239e                    ___ \u239b  ___   ___\u239e                   ___ \u239b  ___   ___\u239e   \n \u23a0                4\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0               4\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                 4\u22c5\u0393(5/4)                     \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n5\u22c5\u2148\u22c5\u03c0\u239e                   \u239b   \u239b               \u2148\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0       \u239b               \n\u2500\u2500\u2500\u2500\u2500\u239f  -5\u22c5\u2148\u22c5\u03c0           \u239c   \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500       \u239c               \n 8   \u239f  \u2500\u2500\u2500\u2500\u2500\u2500           \u239c   \u239c    ___   ___   4 \u239f   8         \u239c    ___   ___  \n     \u239f    8          ___ \u239ccos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f       cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f\n\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f         9\u22c5\u2572\u2571 \u03c0 \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     \u239f                   \u239c             _____________                   _______\n     \u239f                   \u239c      ___   \u2571   ___   ___             ___   \u2571   ___ \n     \u23a0                   \u239d    \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w            \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                       ___                    \n                                                     \u2572\u2571 \u03c0                     \n\n\u2148\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0      \u239b               \u2148\u22c5\u03c0\u239e  -3\u22c5\u2148\u22c5\u03c0       \u239b               \u2148\u22c5\u03c0\u239e  -3\u22c5\u2148\u22c5\n\u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500      \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500\u2500\u2500       \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500\u2500\n 4 \u239f   8        \u239c    ___   ___   4 \u239f    8          \u239c    ___   ___   4 \u239f    8  \n   \u23a0\u22c5\u212f       sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f         sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f     \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n______                                3/2                               3/2   \n  ___                ___ \u239b  ___   ___\u239e                 ___ \u239b  ___   ___\u239e      \n\u2572\u2571 w             2\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0             2\u22c5\u2572\u2571 \u03c0 \u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n            7/4  7/4                                                          \n        16\u22c5a   \u22c5w                                                             \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n\u03c0\u239e        \u239e                                                                   \n\u2500\u239f  -7\u22c5\u2148\u22c5\u03c0\u239f                                                                   \n \u239f  \u2500\u2500\u2500\u2500\u2500\u2500\u239f                                                                   \n \u239f    8   \u239f             \u239b   \u239b               \u2148\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0       \u239b               \u2148\n\u2500\u239f\u22c5\u212f      \u239f             \u239c   \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500       \u239c               \u2500\n \u239f        \u239f             \u239c   \u239c    ___   ___   4 \u239f   8         \u239c    ___   ___   \n \u239f        \u239f             \u239csin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f       sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f \n \u23a0        \u239f           \u03c0\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u0393(-3/4)     \u239c              _____________                   _______\n          \u239f             \u239c       ___   \u2571   ___   ___             ___   \u2571   ___ \n          \u23a0             \u239d   4\u22c5\u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w          4\u22c5\u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                      4 ___ 4 ___             \n                                                    2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u0393(3/4)      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n                                                                              \n                                                                              \n                                                                              \n\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0\u239e                 \u239b   \u239b               \u2148\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0       \u239b             \n\u2500\u2500\u239f  \u2500\u2500\u2500\u2500\u239f  -\u2148\u22c5\u03c0           \u239c   \u239c               \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500       \u239c             \n4 \u239f   8  \u239f  \u2500\u2500\u2500\u2500           \u239c   \u239c    ___   ___   4 \u239f   8         \u239c    ___   ___\n  \u23a0\u22c5\u212f    \u239f   8             \u239ccos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u212f       cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f    \u22c5\u0393(-1/4)   \u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n______   \u239f                 \u239c             _____________                   _____\n  ___    \u239f                 \u239c      ___   \u2571   ___   ___             ___   \u2571   __\n\u2572\u2571 w     \u23a0                 \u239d    \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w            \u2572\u2571 \u03c0 \u22c5\u2572\u2571  \u2572\u2571 a\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                4 ___ 4 ___   \n                                                              2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n                                \u239e\n                                \u239f\n                                \u239f\n  \u2148\u22c5\u03c0\u239e  -\u2148\u22c5\u03c0\u239e                   \u239f\n  \u2500\u2500\u2500\u239f  \u2500\u2500\u2500\u2500\u239f  \u2148\u22c5\u03c0              \u239f\n   4 \u239f   8  \u239f  \u2500\u2500\u2500              \u239f\n\u22c5\u212f   \u23a0\u22c5\u212f    \u239f   8               \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u212f   \u22c5\u0393(1/4)\u22c5\u0393(3/4)\u239f\n________    \u239f                   \u239f\n_   ___     \u239f                   \u239f\n \u22c5\u2572\u2571 w      \u23a0                   \u239f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                                \u239f\n                                \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                 \n                                 "
      }
     ],
     "prompt_number": 178
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 179,
       "text": "\n                \u239b                       \u239b               \u2148\u22c5\u03c0\u239e                  \n                \u239c                       \u239c               \u2500\u2500\u2500\u239f                  \n  ___  5/4  7/4 \u239c      3/4   ___        \u239c    ___   ___   4 \u239f     4 ____   ___ \n\u2572\u2571 2 \u22c5a   \u22c5w   \u22c5\u239d4\u22c5(-1)   \u22c5\u2572\u2571 2 \u22c5a\u22c5w\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 + 4\u22c5\u2572\u2571 -1 \u22c5\u2572\u2571 2 \u22c5\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n                                                                              \n\n       \u239b               \u2148\u22c5\u03c0\u239e            \u239b               \u2148\u22c5\u03c0\u239e                   \n       \u239c               \u2500\u2500\u2500\u239f            \u239c               \u2500\u2500\u2500\u239f                   \n       \u239c    ___   ___   4 \u239f            \u239c    ___   ___   4 \u239f     4 ____   ___  \na\u22c5w\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 + 8\u22c5a\u22c5w\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 - 4\u22c5\u2572\u2571 -1 \u22c5\u2572\u2571 2 \u22c5a\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                            11/2              \n                                               \u239b  ___   ___\u239e                  \n                                            16\u22c5\u239d\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0                  \n\n       \u239b               \u2148\u22c5\u03c0\u239e                           \u239b               \u2148\u22c5\u03c0\u239e    \n       \u239c               \u2500\u2500\u2500\u239f                           \u239c               \u2500\u2500\u2500\u239f    \n       \u239c    ___   ___   4 \u239f         3/4   ___         \u239c    ___   ___   4 \u239f    \n\u22c5w\u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 + 4\u22c5(-1)   \u22c5\u2572\u2571 2 \u22c5a\u22c5w\u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0 + 8\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n                                                                              \n\n         \u239b               \u2148\u22c5\u03c0\u239e\u239e\n         \u239c               \u2500\u2500\u2500\u239f\u239f\n         \u239c    ___   ___   4 \u239f\u239f\n\u22c5a\u22c5w\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                              \n                              \n                              "
      }
     ],
     "prompt_number": 179
    },
    {
     "cell_type": "markdown",
     "source": "27"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(t)/sqrt(t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADAAAAAsBAMAAADROCZUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQdX/AQ0ecgPdBTJ+AAAAAElFTkSuQmCC\n",
       "prompt_number": 180,
       "text": "\nlog(t)\n\u2500\u2500\u2500\u2500\u2500\u2500\n  ___ \n\u2572\u2571 t  "
      }
     ],
     "prompt_number": 180
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 181,
       "text": "\n                                                                       \u239b      \n                                               ___   ___        2  \u250c\u2500  \u239c   1/4\n                                             \u2572\u2571 2 \u22c5\u2572\u2571 w \u22c5\u0393(-1/4) \u22c5 \u251c\u2500  \u239c      \n                     \u239b              \u2502   2\u239e                        2\u2575 3 \u239d1/2, 5\n    ___       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -w \u239f   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  \u2572\u2571 2 \u22c5\u0393(1/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f                       ___       2  \n                2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                   4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(3/4)   \n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                  ___       2                                                 \n              4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(5/4)                                                  \n\n        \u2502   2\u239e      \u239b 2\u239e                            \n, 1/4   \u2502 -w \u239f      \u239cw \u239f                            \n        \u2502 \u2500\u2500\u2500\u239f   log\u239c\u2500\u2500\u239f                            \n/4, 5/4 \u2502  4 \u23a0      \u239d4 \u23a0              \u03c0             \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500 - 3\u22c5log(2) - \u2500 - EulerGamma\n                    2                 2             \n                                                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n         ___                                        \n       \u2572\u2571 w                                         "
      }
     ],
     "prompt_number": 181
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "hyperexpand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 182,
       "text": "\n                                                                       \u239b      \n                                               ___   ___        2  \u250c\u2500  \u239c   1/4\n                                             \u2572\u2571 2 \u22c5\u2572\u2571 w \u22c5\u0393(-1/4) \u22c5 \u251c\u2500  \u239c      \n                     \u239b              \u2502   2\u239e                        2\u2575 3 \u239d1/2, 5\n    ___       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -w \u239f   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  \u2572\u2571 2 \u22c5\u0393(1/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f                       ___       2  \n                2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                   4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(3/4)   \n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                  ___       2                                                 \n              4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(5/4)                                                  \n\n        \u2502   2\u239e      \u239b 2\u239e                            \n, 1/4   \u2502 -w \u239f      \u239cw \u239f                            \n        \u2502 \u2500\u2500\u2500\u239f   log\u239c\u2500\u2500\u239f                            \n/4, 5/4 \u2502  4 \u23a0      \u239d4 \u23a0              \u03c0             \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500 - 3\u22c5log(2) - \u2500 - EulerGamma\n                    2                 2             \n                                                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n         ___                                        \n       \u2572\u2571 w                                         "
      }
     ],
     "prompt_number": 182
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 183,
       "text": "\n                     \u239b              \u2502   2\u239e                       \u239b            \n    ___       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -w \u239f     ___        2  \u250c\u2500  \u239c   1/4, 1/4 \n  \u2572\u2571 2 \u22c5\u0393(1/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f   \u2572\u2571 2 \u22c5\u0393(-1/4) \u22c5 \u251c\u2500  \u239c            \n                2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                  2\u2575 3 \u239d1/2, 5/4, 5/\n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                  ___       2                                 ___       2     \n              4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(5/4)                              4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(3/4)      \n\n  \u2502   2\u239e                                            \n  \u2502 -w \u239f                                            \n  \u2502 \u2500\u2500\u2500\u239f      \u239b 2\u239e                                  \n4 \u2502  4 \u23a0   log\u239dw \u23a0      \u03c0      2\u22c5log(2)   EulerGamma\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               ___       ___      ___         ___   \n           2\u22c5\u2572\u2571 w    2\u22c5\u2572\u2571 w     \u2572\u2571 w        \u2572\u2571 w    "
      }
     ],
     "prompt_number": 183
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 184,
       "text": "\n \u239b                                    \u239b              \u2502   2\u239e                   \n \u239c    ___   ___        2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -w \u239f     ___   ___     \n-\u239c- \u2572\u2571 2 \u22c5\u2572\u2571 w \u22c5\u0393(-1/4) \u22c5\u0393(5/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f + \u2572\u2571 2 \u22c5\u2572\u2571 w \u22c5\u0393(1/\n \u239d                               2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                   \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n                 \u239b              \u2502   2\u239e                                        \n  2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -w \u239f       ___    \u239b 2\u239e       2       2      \n4) \u22c5\u0393(3/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f + 2\u22c5\u2572\u2571 \u03c0 \u22c5log\u239dw \u23a0\u22c5\u0393(3/4) \u22c5\u0393(5/4)  + 4\u22c5E\n            2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                                        \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                  ___   ___       2       2                   \n                              4\u22c5\u2572\u2571 \u03c0 \u22c5\u2572\u2571 w \u22c5\u0393(3/4) \u22c5\u0393(5/4)                    \n\n                                                                              \n            ___       2       2       ___              2       2      3/2     \nulerGamma\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(3/4) \u22c5\u0393(5/4)  + 8\u22c5\u2572\u2571 \u03c0 \u22c5log(2)\u22c5\u0393(3/4) \u22c5\u0393(5/4)  + 2\u22c5\u03c0   \u22c5\u0393(3/\n                                                                              \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n           \u239e\n  2       2\u239f\n4) \u22c5\u0393(5/4) \u239f\n           \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n            \n            "
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAO8AAAAvBAMAAAD5toA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nX8dd98pw8yhBa1IAAAAASUVORK5CYII=\n",
       "prompt_number": 185,
       "text": "\n \u239b   \u239b 2\u239e                              \u239e\n-\u239dlog\u239dw \u23a0 + 2\u22c5EulerGamma + 4\u22c5log(2) + \u03c0\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                    ___                 \n                2\u22c5\u2572\u2571 w                  "
      }
     ],
     "prompt_number": 185
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA4oAAABJCAMAAABMxyhNAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nEg4AAAAASUVORK5CYII=\n",
       "prompt_number": 186,
       "text": "\n \u239b                                   \u239b              \u2502   2\u239e                    \n \u239c    ___   ___       2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -t \u239f     ___   ___      \n-\u239c- \u2572\u2571 2 \u22c5\u2572\u2571 t \u22c5\u0393(1/4) \u22c5\u0393(3/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f + \u2572\u2571 2 \u22c5\u2572\u2571 t \u22c5\u0393(-1/\n \u239d                              2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                 ___   ___    \n                                                             4\u22c5\u2572\u2571 \u03c0 \u22c5\u2572\u2571 t \u22c5\u0393(3\n\n                 \u239b              \u2502   2\u239e                                  \u239e\n  2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -t \u239f       ___    \u239b 2\u239e       2       2\u239f\n4) \u22c5\u0393(5/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f - 2\u22c5\u2572\u2571 \u03c0 \u22c5log\u239dt \u23a0\u22c5\u0393(3/4) \u22c5\u0393(5/4) \u239f\n            2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                                  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   2       2                                                             \n/4) \u22c5\u0393(5/4)                                                              "
      }
     ],
     "prompt_number": 186
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAABJCAMAAAAuTVMOAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nau5/EPZFVh6hXhsbel9evkbtXiD8B2/6pWOqCItRAAAAAElFTkSuQmCC\n",
       "prompt_number": 187,
       "text": "\n                      \u239b              \u2502   2\u239e                      \u239b            \n    ___        2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -t \u239f     ___       2  \u250c\u2500  \u239c   1/4, 1/4 \n  \u2572\u2571 2 \u22c5\u0393(-1/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f   \u2572\u2571 2 \u22c5\u0393(1/4) \u22c5 \u251c\u2500  \u239c            \n                 2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                 2\u2575 3 \u239d1/2, 5/4, 5/\n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                   ___       2                                ___       2     \n               4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(3/4)                             4\u22c5\u2572\u2571 \u03c0 \u22c5\u0393(5/4)      \n\n  \u2502   2\u239e          \n  \u2502 -t \u239f          \n  \u2502 \u2500\u2500\u2500\u239f      \u239b 2\u239e\n4 \u2502  4 \u23a0   log\u239dt \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               ___\n           2\u22c5\u2572\u2571 t "
      }
     ],
     "prompt_number": 187
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 188,
       "text": "\n \u239b                                   \u239b              \u2502   2\u239e                    \n \u239c    ___   ___       2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -t \u239f     ___   ___      \n-\u239c- \u2572\u2571 2 \u22c5\u2572\u2571 t \u22c5\u0393(1/4) \u22c5\u0393(3/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f + \u2572\u2571 2 \u22c5\u2572\u2571 t \u22c5\u0393(-1/\n \u239d                              2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                 ___   ___    \n                                                             4\u22c5\u2572\u2571 \u03c0 \u22c5\u2572\u2571 t \u22c5\u0393(3\n\n                 \u239b              \u2502   2\u239e                                  \u239e\n  2       2  \u250c\u2500  \u239c   1/4, 1/4   \u2502 -t \u239f       ___    \u239b 2\u239e       2       2\u239f\n4) \u22c5\u0393(5/4) \u22c5 \u251c\u2500  \u239c              \u2502 \u2500\u2500\u2500\u239f - 2\u22c5\u2572\u2571 \u03c0 \u22c5log\u239dt \u23a0\u22c5\u0393(3/4) \u22c5\u0393(5/4) \u239f\n            2\u2575 3 \u239d1/2, 5/4, 5/4 \u2502  4 \u23a0                                  \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   2       2                                                             \n/4) \u22c5\u0393(5/4)                                                              "
      }
     ],
     "prompt_number": 188
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADoAAAAvBAMAAABAjsQzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRRM10ukNW5m+9D3T5KT9M2dlDTfbAH8Bd0+UPnD3AeYAAAAASUVORK5CYII=\n",
       "prompt_number": 189,
       "text": "\n   \u239b 2\u239e\nlog\u239dt \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    ___\n2\u22c5\u2572\u2571 t "
      }
     ],
     "prompt_number": 189
    },
    {
     "cell_type": "markdown",
     "source": "28"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(t**2-a**2)*log(t/a)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEUAAAArBAMAAADcXVgwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIjK7q81UdmaJmd3v\nRBCBhf8tAAACQElEQVQ4EZ1UQWsTQRT+dtMma5psFkHwtnNQe1BIJYfe7OJF9OKtHnpZRFDpZaFC\nYkEJXqxFao4VPBQPNtZL8aBelPwBJYioeFq99CSJXkXjezuzs5kkVegHee973/vyZrMzE2ACDgOu\nAL5PaKWSFQDFJlAIU2U852JgxiP9zFCPZg+jDpQf3SLlWKbaCyIriL2hzxVWkmFMCBWRJBXyc0Ta\nXBRaSqJkeqa489ylUO5QUDA9M12S++8puH9SRzLn6t0mivXNmyRWPArtkNtvOUhUxKEtPMQF7Ngk\n+LGSgVea0fP4HnzvJe6zVs0alzJaEQ9oieYKzqeeAYH4mCf6XA/ZM7TWC64laC0BX6i30eNnljCf\nOcAOGnHSKfFvl/iREtgXF7G+2kRv8CsiMcchgd1RRCfrNL4tUuUEFOortGLCdJ9JPgCeUHY7dHyi\nHrFpQcHE9ca9kBUy+vFxIie5mowcsAzelceT+6yWW/iA103O++MyimurIfb2dxysw7v3b/QPNvg/\n37LrZ0cdszeEKe3hVGwqbmS/M5UqKl1Tsfv4PaJg6HxRyxIQbnaGlPmpzCdkytFmFEc3xNmSzWsy\n8crrkmbxE+KkUB66ReWIL7VCobEM+/ZRkZTS82VpG7Nf76QOYB7P4CeXijQ1Zx7WYNDXHmeXLoaG\n8vxUglVjRKUW0gtXrNWWarUAoJdjwO8O/5HIOc6cYUE1dnZDLUnPVJTXCpOSdySItCI90+GGVpiU\n2xvnPK1IT35baGWcfDSkv9cMmJ08I9alAAAAAElFTkSuQmCC\n",
       "prompt_number": 190,
       "text": "\n     \u239bt\u239e \n  log\u239c\u2500\u239f \n     \u239da\u23a0 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   2    2\n- a  + t "
      }
     ],
     "prompt_number": 190
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 191
    },
    {
     "cell_type": "markdown",
     "source": "29"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/(t**2-a**2)*log(b*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEUAAAAoBAMAAABaySqeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
       "prompt_number": 192,
       "text": "\n log(b\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   2    2\n- a  + t "
      }
     ],
     "prompt_number": 192
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 193
    },
    {
     "cell_type": "markdown",
     "source": "30"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/t*log(1+t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAE8AAAAnBAMAAAC8vQiCAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 194,
       "text": "\nlog(t + 1)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    t     "
      }
     ],
     "prompt_number": 194
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 195
    },
    {
     "cell_type": "markdown",
     "source": "31"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(Abs((a+t)/(b-t)))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAAAsBAMAAABlMtBbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n5/jmGiUAAAAASUVORK5CYII=\n",
       "prompt_number": 196,
       "text": "\n   \u239b\u2502a + t\u2502\u239e\nlog\u239c\u2502\u2500\u2500\u2500\u2500\u2500\u2502\u239f\n   \u239d\u2502b - t\u2502\u23a0"
      }
     ],
     "prompt_number": 196
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 197
    },
    {
     "cell_type": "markdown",
     "source": "32"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t)*log(t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFIAAAAUBAMAAADsA3fZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nbeEXwDZUhgJ3ZT0AAAAASUVORK5CYII=\n",
       "prompt_number": 198,
       "text": "\n -a\u22c5t       \n\u212f    \u22c5log(t)"
      }
     ],
     "prompt_number": 198
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception!",
     "language": "python",
     "outputs": [],
     "prompt_number": 199
    },
    {
     "cell_type": "markdown",
     "source": "33"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log((a**2+t**2)/(b**2+t**2))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGwAAAAtBAMAAAC5TJM3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 200,
       "text": "\n   \u239b 2    2\u239e\n   \u239ca  + t \u239f\nlog\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n   \u239c 2    2\u239f\n   \u239db  + t \u23a0"
      }
     ],
     "prompt_number": 200
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 201
    },
    {
     "cell_type": "markdown",
     "source": "34"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(Abs((a**2+t**2)/(b**2-t**2)))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHYAAAAtBAMAAACJwIIWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwXyc3SuCP7UG6Da/mVabAAAAAElFTkSuQmCC\n",
       "prompt_number": 202,
       "text": "\n   \u239b\u2502 2    2\u2502\u239e\n   \u239c\u2502a  + t \u2502\u239f\nlog\u239c\u2502\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2502\u239f\n   \u239c\u2502 2    2\u2502\u239f\n   \u239d\u2502b  - t \u2502\u23a0"
      }
     ],
     "prompt_number": 202
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 203
    },
    {
     "cell_type": "markdown",
     "source": "35"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/t*log((a+t)/(a-t))**2",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAAA1BAMAAAAt7dENAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 204,
       "text": "\n   2       \n    \u239ba + t\u239e\nlog \u239c\u2500\u2500\u2500\u2500\u2500\u239f\n    \u239da - t\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     t     "
      }
     ],
     "prompt_number": 204
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 205
    },
    {
     "cell_type": "markdown",
     "source": "36"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(a**2+t**2)/sqrt(a**2+t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGIAAAAvBAMAAADqTQKPAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
       "prompt_number": 206,
       "text": "\n   \u239b 2    2\u239e\nlog\u239da  + t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   _________\n  \u2571  2    2 \n\u2572\u2571  a  + t  "
      }
     ],
     "prompt_number": 206
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 207
    },
    {
     "cell_type": "markdown",
     "source": "37"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(1+a**2/t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAAAtBAMAAACubgP+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIjK7q81UdmaJmd3v\nRBCBhf8tAAACwElEQVRIDY2VTWgTQRTH326STbJhN0ER1IsLKkUQWoj142Tx4tWDCF5kD5704Cpi\nK4gGBVssSA5F8eMQkFK9BRSEnuLNeii5CV6yQsGDSJqAbT3U9b3Z2dndmQ3xHfL+7/eftzs7mZ0F\nGBkTt52RnmxoXUZsT1+XLfilkBDs81nWN2FXGWE2FETAvsKxYw/UASdVhKTgRthsRirOP2uxjtWS\nkE+EioXVjrVQ8YNbni1oLE7FUqgcm9Ds4zZMfH8oaCwm/VhHirGcZ7a1INiMYCKH10wAlCeoXASz\nRTkjLPVC9pDGrUHFzRjP0GfFKHYQabvQ9xWLg2XFKMwg0v/CoqFYHPR82em7RD5pF4uyE9VVN1JR\nvuGT+rawcTMicq40QXNS8HWqyiryU3CYLZQwp4VSxUaXWBEXO93zQR0KusvgsQcsG7jb0z1rGT1G\nI4Th0+v4VqV7dsb2aFvUY8zNAazcnW/ieARKpO9j42WH8BLKzXzLbDm4A8b3wDb2aAPQBhWv1MEb\n0GSVSN8H/mBPCRdvpziVp6mFPdWABzrwpj79vs52O98BUc+2NX+Hrv/fcxuCNixTBx4649cN2Bos\n4RtWfBo2xT367LkQQfp57C048tstrbwFOwg+0hBcFB4/4LgfSt5z4OxqFwG+XDz21uyjLuovvN4D\nk1ClIRiWyxL/scRJeRXAJKvOnTOgQ7/Gi1SiZQ7DeL7wjNQ9XtME3nGdTmY7XQP0fEbwgIdSSzZZ\nnZuRcb9LxFpe9eAr+LJLdbUh00qTkZwH+v39juxS3avJtNxmpOrAoSCQTVa/UqgeruSkYghwWSgh\n2D8Lj0QtCzz7lLjOyHlwFScEeOwoUWkQulTyKWVE1h9tdGjgtVv0mxXxZzDhnk5oVWrrKgPI/spG\nIwvdSCWzdSFZyfqFDMIat/jIMFrZVvRaZrkHCf4DWxGt3CceTukAAAAASUVORK5CYII=\n",
       "prompt_number": 208,
       "text": "\n   \u239b 2    \u239e\n   \u239ca     \u239f\nlog\u239c\u2500\u2500 + 1\u239f\n   \u239c 2    \u239f\n   \u239dt     \u23a0"
      }
     ],
     "prompt_number": 208
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 209
    },
    {
     "cell_type": "markdown",
     "source": "38"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "log(Abs(1-a**2/t**2))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAtBAMAAAB11ancAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 210,
       "text": "\n   \u239b\u2502   2    \u2502\u239e\n   \u239c\u2502  a     \u2502\u239f\nlog\u239c\u2502- \u2500\u2500 + 1\u2502\u239f\n   \u239c\u2502   2    \u2502\u239f\n   \u239d\u2502  t     \u2502\u23a0"
      }
     ],
     "prompt_number": 210
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 211
    },
    {
     "cell_type": "markdown",
     "source": "39"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADgAAAAnBAMAAACoKJZjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZlTNRImrEN27MiJ2\n75lZwTvPAAABX0lEQVQ4Ea2SMUvDQBiG36TxorElVsGCKBRdxE0QdAyI4CQd/AH+ACGZ3LTBX+Ao\n4nAgCE4NuriUJpO/w82hiKIgVKF+d81dU+Gc8kLu3u97wpfL8QKTmtPl2KkWS5TDWe5WItWaz80s\nh52O/JqGcQ5nWsB27tWm3oYfAJnq5jujnlSH1hvAWl3wLvnud71PtU9PNVvHwQ5VVOyBRW3u/qBH\nH24TvMaLWIBahP3Agc/xLhZ0aVKMV2BAcDoBG16J/kCe4ZHeb+Ec3puAHNF9mGh4CvQC9wvWxWjs\nEqZSDekMnciKmyy15YEWUQ0IfsqxFY5a8nCUVpoN4A5YzjIv3Lr92Ag36TdSOM+N48Tuc6BOo4ty\n40L19/pwOIYOXe+kGN1ErhNl9O6m2j5pV7oZ/qPSP1buQMqyWSLLRoksGyWybJLMsgnKLBuhyLJJ\nMssmKLNsgjLLJiizbIIyywX4Cy0DaRmSOuonAAAAAElFTkSuQmCC\n",
       "prompt_number": 212,
       "text": "\nsin(a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   t    "
      }
     ],
     "prompt_number": 212
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAcEAAAClCAMAAAATd7YiAAAAQlBMVEX///8AAAAAAAAAAAAAAAAA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\ncHuzWlI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       "prompt_number": 213,
       "text": "\n\u23a7                                                        \u2502 2\u2502    \n\u23aa                                                        \u2502a \u2502    \n\u23aa                        0                           for \u2502\u2500\u2500\u2502 < 1\n\u23aa                                                        \u2502 2\u2502    \n\u23aa                                                        \u2502w \u2502    \n\u23aa                                                                \n\u23aa                     ___   ___                          \u2502 2\u2502    \n\u23aa                   \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0                           \u2502w \u2502    \n\u23aa                   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500                      for \u2502\u2500\u2500\u2502 < 1\n\u23aa                        2                               \u2502 2\u2502    \n\u23aa                                                        \u2502a \u2502    \n\u23aa                                                                \n\u23aa            \u23a7                             \u2502 2\u2502                  \n\u23aa  ___   ___ \u23aa                             \u2502a \u2502                  \n\u23aa\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5\u23aa           0             for \u2502\u2500\u2500\u2502 < 1              \n\u23a8            \u23aa                             \u2502 2\u2502                  \n\u23aa            \u23aa                             \u2502w \u2502                  \n\u23aa            \u23aa                                                   \n\u23aa            \u23aa                             \u2502 2\u2502                  \n\u23aa            \u23aa                             \u2502w \u2502                  \n\u23aa            \u23a8           1             for \u2502\u2500\u2500\u2502 < 1              \n\u23aa            \u23aa                             \u2502 2\u2502                  \n\u23aa            \u23aa                             \u2502a \u2502                  \n\u23aa            \u23aa                                                   \n\u23aa            \u23aa        \u239b         \u2502  2\u239e                            \n\u23aa            \u23aa\u256d\u2500\u256e1, 1 \u239c 1   1/2 \u2502 a \u239f                            \n\u23aa            \u23aa\u2502\u2576\u2510     \u239c         \u2502 \u2500\u2500\u239f   otherwise                \n\u23aa            \u23aa\u2570\u2500\u256f2, 2 \u239c1/2   0  \u2502  2\u239f                            \n\u23aa            \u23a9        \u239d         \u2502 w \u23a0                            \n\u23aa\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500   otherwise  \n\u23a9                        2                                       "
      }
     ],
     "prompt_number": 213
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "inverse_cosine_transform(sqrt(2)*sqrt(pi)/2, w, t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEEAAAAnBAMAAACidDgxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nMJSNTHwDq9dxcD68zdEAAAAASUVORK5CYII=\n",
       "prompt_number": 214,
       "text": "\nsin(\u221e\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n   t    "
      }
     ],
     "prompt_number": 214
    },
    {
     "cell_type": "markdown",
     "source": "40"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t*sin(a*t)/(t**2+b**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEIAAAAoBAMAAAC4FTHnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 215,
       "text": "\nt\u22c5sin(a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  2    2  \n b  + t   "
      }
     ],
     "prompt_number": 215
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 216
    },
    {
     "cell_type": "markdown",
     "source": "41"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)/(t*(t**2+b**2))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAE0AAAArBAMAAADPihjEAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZlTNRImrEN27MiJ2\n75lZwTvPAAACbklEQVQ4EcWUP2gTURzHv5eed/HSNq1FC0Ul6iJuQsFuBkXoIJJBcM0sYm5y8c8F\nZ4eORjo8LAhCJacuLpLLYhcnF8FJB8EhSIsBoRHO3++9e7+7NEFcxB/ce9/3+36593J3nwBTakF6\nuZJWLrxY9ANRIk6EVh7JREWhlNimzGck1856hxvABfEnhNyjWgf6E7Y0PLJ1dWncyrSZnNNLwWN1\nebQ4oHWVrtn+WVxboxUv8roCL4yU/ws9OmRE/U184wGYk1Nzer3uoqqwxwPeAk4b34F9csox+7a8\n9AlH9sFHf0N3aeAhgl2yy8pmeA5ftWLJ3Qd6df8nnA1yxvddwaFEcnT0bui0a15SOvg7jmG2Trmh\n3ndGYS5+3UxmasvAc95O6ni/H7RWn/041zpPzySB+2X5VlwaKGBRMhPCbxdaf3hvuJ7n3EauJ5QX\nSuuOqCnCT6S5I+p/ifSvil/1v6vg/c2DN99+p8ZaC7y6hxf5I9a2nwQfoT2T9uLgokJXfy+mY0b6\nVocwsBPNAKFNdAWI4mKKLOWPMtiZZrSBJU585QF4aia25unSHw0jwWjfJs/5TAPVKTOxdZKkhp32\nA6P9gearCGmUHFlu4hvYLc2VvaNJsPNSFXJsbd9dySBhmgltZ4hPvTTVMbvvJippuptBxzQT2l4T\nj0yIxux8bHEx7JpmRrtGfwe65judtU6nmVncYtg1zYR2FLsj7uky99MWrxl2S3PEO9syOW1xi8iH\nppnQLmPdPBM2TE5bvGTYNc2EdjC4wS1TJqctbgjsY2iTccnE7ZjDXkDbmvlcgL2Adu5bVYDdT2xz\nysyw/waVILmNqfdBaQAAAABJRU5ErkJggg==\n",
       "prompt_number": 217,
       "text": "\n  sin(a\u22c5t) \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  \u239b 2    2\u239e\nt\u22c5\u239db  + t \u23a0"
      }
     ],
     "prompt_number": 217
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 218
    },
    {
     "cell_type": "markdown",
     "source": "42"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-b*t)*sin(a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAUBAMAAAD/1DctAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 219,
       "text": "\n -b\u22c5t         \n\u212f    \u22c5sin(a\u22c5t)"
      }
     ],
     "prompt_number": 219
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception!",
     "language": "python",
     "outputs": [],
     "prompt_number": 220
    },
    {
     "cell_type": "markdown",
     "source": "43"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-t)*sin(t)/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEsAAAApBAMAAACPXMmIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 221,
       "text": "\n -t       \n\u212f  \u22c5sin(t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    t     "
      }
     ],
     "prompt_number": 221
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception!",
     "language": "python",
     "outputs": [],
     "prompt_number": 222
    },
    {
     "cell_type": "markdown",
     "source": "44"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)**2/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAoBAMAAAC84OHaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nIMKgM4gw6AwiDCnDNwqPeYYvFsSlAAAAAElFTkSuQmCC\n",
       "prompt_number": 223,
       "text": "\n   2     \nsin (a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    t    "
      }
     ],
     "prompt_number": 223
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 224
    },
    {
     "cell_type": "markdown",
     "source": "45"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)*sin(b*t)/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAnBAMAAADKh7oJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nXf9ZvwAYTc/gwuHGFgAAAABJRU5ErkJggg==\n",
       "prompt_number": 225,
       "text": "\nsin(a\u22c5t)\u22c5sin(b\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n        t        "
      }
     ],
     "prompt_number": 225
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 226
    },
    {
     "cell_type": "markdown",
     "source": "46"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)**2/t**2",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAoBAMAAAC84OHaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "prompt_number": 227,
       "text": "\n   2     \nsin (a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     2   \n    t    "
      }
     ],
     "prompt_number": 227
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKQAAAAtBAMAAADSJN1iAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 228,
       "text": "\n               \u239b   2           \u239e\n               \u239csin (a\u22c5t)      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c     2         \u239f\n               \u239d    t          \u23a0"
      }
     ],
     "prompt_number": 228
    },
    {
     "cell_type": "markdown",
     "source": "47"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)**3/t**2",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAoBAMAAAC84OHaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
       "prompt_number": 229,
       "text": "\n   3     \nsin (a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     2   \n    t    "
      }
     ],
     "prompt_number": 229
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 230
    },
    {
     "cell_type": "markdown",
     "source": "48"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t)**3/t**3",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAoBAMAAAC84OHaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
       "prompt_number": 231,
       "text": "\n   3     \nsin (a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     3   \n    t    "
      }
     ],
     "prompt_number": 231
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 232
    },
    {
     "cell_type": "markdown",
     "source": "49"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(1-cos(a*t))/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAnBAMAAAD6C6soAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNQAAAABJRU5ErkJggg==\n",
       "prompt_number": 233,
       "text": "\n-cos(a\u22c5t) + 1\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n      t      "
      }
     ],
     "prompt_number": 233
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAASIAAAAsBAMAAAAz7ahBAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
       "prompt_number": 234,
       "text": "\n               \u239b1      \u239e                  \u239bcos(a\u22c5t)      \u239e\nCosineTransform\u239c\u2500, t, w\u239f - CosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239dt      \u23a0                  \u239d   t          \u23a0"
      }
     ],
     "prompt_number": 234
    },
    {
     "cell_type": "markdown",
     "source": "50"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(1-cos(a*t))/t**2",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAnBAMAAAD6C6soAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 235,
       "text": "\n-cos(a\u22c5t) + 1\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n       2     \n      t      "
      }
     ],
     "prompt_number": 235
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAASoAAAAsBAMAAAAgOui1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\noTpxVAcijx0tyta66LpfTNSNdb+Y/AMN3o1BPIriFgAAAABJRU5ErkJggg==\n",
       "prompt_number": 236,
       "text": "\n               \u239b1       \u239e                  \u239bcos(a\u22c5t)      \u239e\nCosineTransform\u239c\u2500\u2500, t, w\u239f - CosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c 2      \u239f                  \u239c    2         \u239f\n               \u239dt       \u23a0                  \u239d   t          \u23a0"
      }
     ],
     "prompt_number": 236
    },
    {
     "cell_type": "markdown",
     "source": "51"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cos(a*t)/(b**2+t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADoAAAAoBAMAAABdi/SLAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n65SPFWSurPVMNLRtSMJfuZmLdTEugiIAAAAASUVORK5CYII=\n",
       "prompt_number": 237,
       "text": "\ncos(a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2    2 \nb  + t  "
      }
     ],
     "prompt_number": 237
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAsBAMAAABmqRw2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nPpPGbP2+YLZIjD/u99bMYXG/t/4HBsQWBAmd4PUAAAAASUVORK5CYII=\n",
       "prompt_number": 238,
       "text": "\n               \u239bcos(a\u22c5t)      \u239e\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c 2    2       \u239f\n               \u239db  + t        \u23a0"
      }
     ],
     "prompt_number": 238
    },
    {
     "cell_type": "markdown",
     "source": "52"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-b*t)*cos(a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAUBAMAAADyykdqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
       "prompt_number": 239,
       "text": "\n -b\u22c5t         \n\u212f    \u22c5cos(a\u22c5t)"
      }
     ],
     "prompt_number": 239
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception!",
     "language": "python",
     "outputs": [],
     "prompt_number": 240
    },
    {
     "cell_type": "markdown",
     "source": "53"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-b*t**2)*cos(a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGMAAAAYBAMAAAAc8F6kAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZnaZIruJ70QQVKsy\n3c2S+EuhAAAB1klEQVQ4EZWSv2vUYBjHP+ldr0mu16t1sSqS4FIHpcnVUXgRoSDoVQdxcAgoKLh0\ncHELCE4KoRUcRJpNqAhH/wGzCAXB3iji4OogVOlSOajPJXe5935g9IH3zff5vN/n/ZUXhsM+Oz8M\nirMNHhWbhh0fuT0MijOLx8Wm3PFGYSVU/ucsL6E0z3Y+xT+It1BTZrw7wTpYeaC6tovHd+8vNY8O\nx0uqKmebueqKz+aaLDQpTvZgOcF2Mm00Gg3PWre/eZMKoN3D0wF81yxmqxR8tTSQy/7M1ENwcwyz\nrdfR/jMN5LIqzjT2pP8kzXBXMuCv4MWZtH0X23Uxts8IqEubct/x5IefJbe4nPm0/gKryV0qwVOq\nEWzJyE0udTuYiaisc08zp9L6zeaLA8oHz0NTwKpspU0DOpLUFPUbrkp9WmfKmLEPP6tHdwRfk7kD\nvjAriFpCM9S8Pdkv+RVdfa9AXlIztA4x1mRcNrYlj3G0SDbGlQ7lzmkqTnrivchox1XHTpPpmBOj\nJZzHUA8pLZ9iKoS5hBl1veXMxYvwASxvQY2V2DtLGL7Hgly0XLCD6S3uKNtP4NiYeRKw2hrVH4yG\nR+WDATCDgf6b6v7PXrzqi4Kv5eSGc/AHo7dYuZA0BtwAAAAASUVORK5CYII=\n",
       "prompt_number": 241,
       "text": "\n     2         \n -b\u22c5t          \n\u212f     \u22c5cos(a\u22c5t)"
      }
     ],
     "prompt_number": 241
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 242
    },
    {
     "cell_type": "markdown",
     "source": "54"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t/(b**2+t**2)*tan(a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAoBAMAAACx/pGdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nkxwAAAAASUVORK5CYII=\n",
       "prompt_number": 243,
       "text": "\nt\u22c5tan(a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  2    2  \n b  + t   "
      }
     ],
     "prompt_number": 243
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 244
    },
    {
     "cell_type": "markdown",
     "source": "55"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "t/(b**2+t**2)*cot(a*t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAAoBAMAAAC1C0GgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "prompt_number": 245,
       "text": "\nt\u22c5cot(a\u22c5t)\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  2    2  \n b  + t   "
      }
     ],
     "prompt_number": 245
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [],
     "prompt_number": 246
    },
    {
     "cell_type": "markdown",
     "source": "56"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAD8AAAAWBAMAAACF0lkSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 247,
       "text": "\n   \u239b   2\u239e\nsin\u239da\u22c5t \u23a0"
      }
     ],
     "prompt_number": 247
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAWBAMAAADDSDj9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 248,
       "text": "\n               \u239b   \u239b   2\u239e      \u239e\nCosineTransform\u239dsin\u239da\u22c5t \u23a0, t, w\u23a0"
      }
     ],
     "prompt_number": 248
    },
    {
     "cell_type": "markdown",
     "source": "57"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*(1-t**2))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIEAAAAWBAMAAAAV7eKYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n5VJTiASnhLaFWVKdBPgHB2aCybogJisAAAAASUVORK5CYII=\n",
       "prompt_number": 249,
       "text": "\n   \u239b  \u239b   2    \u239e\u239e\nsin\u239da\u22c5\u239d- t  + 1\u23a0\u23a0"
      }
     ],
     "prompt_number": 249
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAAAWBAMAAACcdXXxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n9tUUjQ86azKNvPz6JkfY2hWrPwPHVtcl1UwJmwAAAABJRU5ErkJggg==\n",
       "prompt_number": 250,
       "text": "\n                \u239b   \u239b   2    \u239e      \u239e\n-CosineTransform\u239dsin\u239da\u22c5t  - a\u23a0, t, w\u23a0"
      }
     ],
     "prompt_number": 250
    },
    {
     "cell_type": "markdown",
     "source": "58"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t**2)/t**2",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAAqBAMAAAAaH/vSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nBpEm9CG/L0yPE0V2fFUAAAAASUVORK5CYII=\n",
       "prompt_number": 251,
       "text": "\n   \u239b   2\u239e\nsin\u239da\u22c5t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     2   \n    t    "
      }
     ],
     "prompt_number": 251
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAAA3BAMAAABqVRwRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 252,
       "text": "\n               \u239b   \u239b   2\u239e      \u239e\n               \u239csin\u239da\u22c5t \u23a0      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c     2         \u239f\n               \u239d    t          \u23a0"
      }
     ],
     "prompt_number": 252
    },
    {
     "cell_type": "markdown",
     "source": "59"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*t**2)/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEMAAAAqBAMAAAAaH/vSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
       "prompt_number": 253,
       "text": "\n   \u239b   2\u239e\nsin\u239da\u22c5t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n    t    "
      }
     ],
     "prompt_number": 253
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAAA3BAMAAABqVRwRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "prompt_number": 254,
       "text": "\n               \u239b   \u239b   2\u239e      \u239e\n               \u239csin\u239da\u22c5t \u23a0      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239d    t          \u23a0"
      }
     ],
     "prompt_number": 254
    },
    {
     "cell_type": "markdown",
     "source": "60"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t**2)*sin(b*t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAAaBAMAAABGGm9mAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 255,
       "text": "\n     2          \n -a\u22c5t     \u239b   2\u239e\n\u212f     \u22c5sin\u239db\u22c5t \u23a0"
      }
     ],
     "prompt_number": 255
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception",
     "language": "python",
     "outputs": [],
     "prompt_number": 256
    },
    {
     "cell_type": "markdown",
     "source": "61"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cos(a*t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEEAAAAWBAMAAABtUuw5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
       "prompt_number": 257,
       "text": "\n   \u239b   2\u239e\ncos\u239da\u22c5t \u23a0"
      }
     ],
     "prompt_number": 257
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAAAWBAMAAAC1cop2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 258,
       "text": "\n               \u239b   \u239b   2\u239e      \u239e\nCosineTransform\u239dcos\u239da\u22c5t \u23a0, t, w\u23a0"
      }
     ],
     "prompt_number": 258
    },
    {
     "cell_type": "markdown",
     "source": "62"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cos(a*(1-t**2))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAAWBAMAAAARGDKlAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVJl2Zs0i7zIQRN2r\nibuk4LwrAAACSklEQVQ4EX1TQWgTURB9adLNJrFJqB4Ei9SioIiyuh6sIK4KgiBa8eIxBwURdXsU\nT3sQelBJoAdBhCx48CTGIoI9SKAXPYgBz0KheBA09iTowfpmk539u6kd2Nn33syf///MLpAxK1Dh\nhiLAdt8bLIJP6EthViW/pZrVVQgsYqFlUIH5Ot2RjCj0m2pVc00TtVAjQyCpqaSBnnc00VVEYKPd\nMLngh3zsrqCUVZKt3yYB6cqhhBI9DYFKg+ANn7TtVppbVYgfQGE6orY0AHh0iu98j+hkxE33Uck2\nSRjaH+AZWkJy3kCqsUR5nvj5gBt+WXElVGivw569Fgg3S5R+U2iz8qTrYftZD6d3zFH5xSd/bBd9\nrUEXWXnfkuNvbETYLIF7lIoh8nPW3YlpfCn38AGwpPAaDtL7LD+0qhOj1CnwmnLFQ7teOuA34N9c\nRsgZrbNxHcww1tRlqAWKU6e4QnncwUuGL/HY3qe/RFKi2MMrxqTEnT5tLal2uP/1Xf87A6jV6TIl\nZq0p9kEu4odRn4yLXJRFA0udQnaq1HkRWH4A/36Az/xtWKbZKnS4h/E1rkD2jCxVIm5nB+cmupgp\ndHGCSVSLjetdJ2r1cBkuF1oxTJWQ8cngptwQZ456BZeDlWmgvPf8CnVjDJPHGRnYsMTtn0sh7Hlq\nC3FE3xcU8VibWFmvxNFJRrIgzn4cA5Rkjy1tPGD46kjKWLLLnpFgRnhAbncyIumqSlVF/wH7qY8F\no8EXKvGT39KieJKe5OYCxTsVbQoWqZYc4B+zdHtmhnDljAAAAABJRU5ErkJggg==\n",
       "prompt_number": 259,
       "text": "\n   \u239b  \u239b   2    \u239e\u239e\ncos\u239da\u22c5\u239d- t  + 1\u23a0\u23a0"
      }
     ],
     "prompt_number": 259
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMAAAAAWBAMAAABklY4GAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\niSy7MChj6sD/qiLkYTmOAbsAAAAASUVORK5CYII=\n",
       "prompt_number": 260,
       "text": "\n               \u239b   \u239b   2    \u239e      \u239e\nCosineTransform\u239dcos\u239da\u22c5t  - a\u23a0, t, w\u23a0"
      }
     ],
     "prompt_number": 260
    },
    {
     "cell_type": "markdown",
     "source": "63"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t**2)*cos(b*t**2)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAaBAMAAABC779bAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 261,
       "text": "\n     2          \n -a\u22c5t     \u239b   2\u239e\n\u212f     \u22c5cos\u239db\u22c5t \u23a0"
      }
     ],
     "prompt_number": 261
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception",
     "language": "python",
     "outputs": [],
     "prompt_number": 262
    },
    {
     "cell_type": "markdown",
     "source": "64"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/t*sin(a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADYAAAAqBAMAAAAKf7UOAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nX2ZtUoDUhsIAAAAASUVORK5CYII=\n",
       "prompt_number": 263,
       "text": "\n   \u239ba\u239e\nsin\u239c\u2500\u239f\n   \u239dt\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\n  t   "
      }
     ],
     "prompt_number": 263
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA3YAAAAsBAMAAADbfjeyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ns747sQzzFesAAAAASUVORK5CYII=\n",
       "prompt_number": 264,
       "text": "\n            \u239b      \u239b       \u239b       ___   ___\u239e          \u239b       ___   ___\u239e     \n            \u239c      \u239cbesseli\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0 + besselj\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   be\n            \u239c  a\u22c5w\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\n            \u239c      \u239c                        2\u22c5a\u22c5w                             \n  ___   ___ \u239c      \u239d                                                          \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n            \u239d                                                           2     \n\n     \u239b       ___   ___\u239e          \u239b       ___   ___\u239e\u239e                          \nsseli\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0 - besselj\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u239f                          \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f                          \n                      3/2  3/2                     \u239f          \u239b       ___   __\n                   2\u22c5a   \u22c5w                        \u23a0   besseli\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                   4          \n\n                              \u239e\n                              \u239f\n                              \u239f\n_\u239e          \u239b       ___   ___\u239e\u239f\n \u23a0   besselj\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u239f\n\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                 4            \u23a0"
      }
     ],
     "prompt_number": 264
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA3YAAAAsBAMAAADbfjeyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ns747sQzzFesAAAAASUVORK5CYII=\n",
       "prompt_number": 265,
       "text": "\n            \u239b      \u239b       \u239b       ___   ___\u239e          \u239b       ___   ___\u239e     \n            \u239c      \u239cbesseli\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0 + besselj\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   be\n            \u239c  a\u22c5w\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\n            \u239c      \u239c                        2\u22c5a\u22c5w                             \n  ___   ___ \u239c      \u239d                                                          \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n            \u239d                                                           2     \n\n     \u239b       ___   ___\u239e          \u239b       ___   ___\u239e\u239e                          \nsseli\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0 - besselj\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u239f                          \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f                          \n                      3/2  3/2                     \u239f          \u239b       ___   __\n                   2\u22c5a   \u22c5w                        \u23a0   besseli\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                   4          \n\n                              \u239e\n                              \u239f\n                              \u239f\n_\u239e          \u239b       ___   ___\u239e\u239f\n \u23a0   besselj\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u239f\n\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n                 4            \u23a0"
      }
     ],
     "prompt_number": 265
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA/wAAAAuBAMAAABnkQ9xAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nZO4Yjl4hR/K4TPwf5kLdQ3hi7w0AAAAASUVORK5CYII=\n",
       "prompt_number": 266,
       "text": "\n  ___   ___        \u239b       ___   ___\u239e     ___   ___        \u239b       ___   ___\u239e \n\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besseli\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besseli\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \n                  4                                       4                   \n                                                                              \n\n    ___   ___        \u239b       ___   ___\u239e     ___   ___        \u239b       ___   ___\n  \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besselj\u239d0, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besselj\u239d2, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \n+ \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                    4                                       4                 \n                                                                              \n\n\u239e     ___   ___        \u239b       ___   ___\u239e     ___   ___        \u239b       ___   _\n\u23a0   \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besseli\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5besselj\u239d1, 2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 \n\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                    ___   ___                               ___   ___         \n                4\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w                            4\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w          \n\n__\u239e\nw \u23a0\n\u2500\u2500\u2500\n   \n   "
      }
     ],
     "prompt_number": 266
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 267
    },
    {
     "cell_type": "markdown",
     "source": "65"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(t)*sin(a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADYAAAAvBAMAAABasiS9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nLGV8yvzwgRKrv5QYvxQ+8ANKSoG5AaaonwAAAABJRU5ErkJggg==\n",
       "prompt_number": 268,
       "text": "\n   \u239ba\u239e\nsin\u239c\u2500\u239f\n   \u239dt\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\n  ___ \n\u2572\u2571 t  "
      }
     ],
     "prompt_number": 268
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 269,
       "text": "\n         \u239b                                       \u2148\u22c5\u03c0                          \n         \u239c                                       \u2500\u2500\u2500                          \n     3/4 \u239c4 ____ 4 ___ 4 ___    \u239b    ___   ___\u239e   4                  4 ____ 4 \n-(-1)   \u22c5\u239d\u2572\u2571 -1 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f   \u22c5\u0393(1/4)\u22c5\u0393(3/4) + \u2572\u2571 -1 \u22c5\u2572\u2571\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n                                                                              \n\n                               \u2148\u22c5\u03c0                                       \u239b    \n                               \u2500\u2500\u2500                      _____________    \u239c    \n___ 4 ___     \u239b    ___   ___\u239e   4                      \u2571   ___   ___     \u239c  __\n a \u22c5\u2572\u2571 w \u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f   \u22c5\u0393(1/4)\u22c5\u0393(3/4) + 2\u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5sin\u239d\u2572\u2571 2\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                           _____________                                      \n                    ___   \u2571   ___   ___                                       \n                8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\u22c5\u0393(5/4)                        \n\n               \u2148\u22c5\u03c0\u239e     \u239b                   \u2148\u22c5\u03c0\u239e               \u239e  -\u2148\u22c5\u03c0\n               \u2500\u2500\u2500\u239f     \u239c                   \u2500\u2500\u2500\u239f               \u239f  \u2500\u2500\u2500\u2500\n_   ___   ___   4 \u239f     \u239c  ___   ___   ___   4 \u239f               \u239f   4  \n \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5sinh\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5\u0393(-1/4)\u22c5\u0393(5/4)\u23a0\u22c5\u212f    \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                      \n                                                                      \n                                                                      "
      }
     ],
     "prompt_number": 269
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA5sAAAA9BAMAAADR6GBNAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfXsbt8NikAAAAABJRU5ErkJggg==\n",
       "prompt_number": 270,
       "text": "\n                                \u2148\u22c5\u03c0                                    \u2148\u22c5\u03c0    \n                                \u2500\u2500\u2500                                    \u2500\u2500\u2500    \n4 ___ 4 ___    \u239b    ___   ___\u239e   4    4 ___ 4 ___     \u239b    ___   ___\u239e   4     \n\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f    + \u2572\u2571 a \u22c5\u2572\u2571 w \u22c5sinh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u212f    + 2\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                        ___   \n                                                                    2\u22c5\u2572\u2571 w \u22c5\u2572\u2571\n\n                             \u239b                   \u2148\u22c5\u03c0\u239e     \u239b                   \n            _____________    \u239c                   \u2500\u2500\u2500\u239f     \u239c                   \n     3/4   \u2571   ___   ___     \u239c  ___   ___   ___   4 \u239f     \u239c  ___   ___   ___  \n\u22c5(-1)   \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5sin\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f   \u23a0\u22c5sinh\u239d\u2572\u2571 2 \u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u22c5\u212f\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n _____________                                                                \n\u2571   ___   ___                                                                 \n  \u2572\u2571 a \u22c5\u2572\u2571 w                                                                  \n\n\u2148\u22c5\u03c0\u239e\n\u2500\u2500\u2500\u239f\n 4 \u239f\n   \u23a0\n\u2500\u2500\u2500\u2500\n    \n    \n    "
      }
     ],
     "prompt_number": 270
    },
    {
     "cell_type": "markdown",
     "source": "66"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(1/sqrt(t))**3*sin(a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADYAAAAuBAMAAACR7vcYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nE36LyDEijgAAAABJRU5ErkJggg==\n",
       "prompt_number": 271,
       "text": "\n   \u239ba\u239e\nsin\u239c\u2500\u239f\n   \u239dt\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\n  3/2 \n t    "
      }
     ],
     "prompt_number": 271
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAzoAAAAzBAMAAACteGDSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n1fT/AAXTH3qwGHFxAAAAAElFTkSuQmCC\n",
       "prompt_number": 272,
       "text": "\n4 ___ \u239b       \u239b    ___   ___\u239e                 \u239b    ___   ___\u239e                \u239b\n\u2572\u2571 w \u22c5\u239d- 3\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4) + 3\u22c5sinh\u239d\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                               _____________  \n                                                      4 ___   \u2571   ___   ___   \n                                                   32\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393\n\n    ___   ___\u239e                  \u239b    ___   ___\u239e       \u239e\n2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                       \n                                                       \n(5/4)                                                  "
      }
     ],
     "prompt_number": 272
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAzoAAAAzBAMAAACteGDSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n1fT/AAXTH3qwGHFxAAAAAElFTkSuQmCC\n",
       "prompt_number": 273,
       "text": "\n4 ___ \u239b       \u239b    ___   ___\u239e                 \u239b    ___   ___\u239e                \u239b\n\u2572\u2571 w \u22c5\u239d- 3\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4) + 3\u22c5sinh\u239d\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                               _____________  \n                                                      4 ___   \u2571   ___   ___   \n                                                   32\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393\n\n    ___   ___\u239e                  \u239b    ___   ___\u239e       \u239e\n2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                       \n                                                       \n(5/4)                                                  "
      }
     ],
     "prompt_number": 273
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
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       "prompt_number": 274,
       "text": "\n4 ___ \u239b       \u239b    ___   ___\u239e                 \u239b    ___   ___\u239e                \u239b\n\u2572\u2571 w \u22c5\u239d- 3\u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4) + 3\u22c5sinh\u239d\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                               _____________  \n                                                      4 ___   \u2571   ___   ___   \n                                                   32\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393\n\n    ___   ___\u239e                  \u239b    ___   ___\u239e       \u239e\n2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4) + 16\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(5/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                       \n                                                       \n(5/4)                                                  "
      }
     ],
     "prompt_number": 274
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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Rg9l4yShKObNXpejQWQsHad9i2dhQN3WRsm0dw49AaXRmqxAXHC8fxp+rqTiDOxq6P+PV\nsczu+16AaykP9FNO9iIHs/GSQKSc3S1pOnRW+I4xlmRQKUe+G+DQmaMOj+R4GcUlScUZ3NHQ/Rmv\njmV238jM3jR5a1f9U2HGkVDNGYzjJYFIObtbpRlK/U+bSiAapRw170OxElo6c9ThkRwvJbP9IBTa\njoZoX150LLP7rrbR9Y30H+6DFGcwjpcDJBzE3TB0ayFIOvMwXK66j2cAdjzXtSzxlR3/v8rl3zk7\nOe6YAAAAAElFTkSuQmCC\n",
       "prompt_number": 275,
       "text": "\n    4 ___    \u239b    ___   ___\u239e           4 ___    \u239b    ___   ___\u239e     4 ___     \n  3\u22c5\u2572\u2571 w \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4)   \u2572\u2571 w \u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   3\u22c5\u2572\u2571 w \u22c5sinh\n- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n               _____________                      _____________               \n      4 ___   \u2571   ___   ___              4 ___   \u2571   ___   ___         4 ___  \n   32\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(5/4)    2\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w       32\u22c5\u2572\u2571 a \u22c5\u2572\n\n\u239b    ___   ___\u239e           4 ___     \u239b    ___   ___\u239e\n\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-3/4)   \u2572\u2571 w \u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n  _____________                       _____________\n \u2571   ___   ___               4 ___   \u2571   ___   ___ \n\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(5/4)     2\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  "
      }
     ],
     "prompt_number": 275
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 276
    },
    {
     "cell_type": "markdown",
     "source": "67"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(t)*cos(a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADgAAAAvBAMAAABEexQOAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nxhHqHNV4U4LoB948fapc4GrbAAAAAElFTkSuQmCC\n",
       "prompt_number": 277,
       "text": "\n   \u239ba\u239e\ncos\u239c\u2500\u239f\n   \u239dt\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\n  ___ \n\u2572\u2571 t  "
      }
     ],
     "prompt_number": 277
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAv4AAAAzBAMAAAAdohHJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 278,
       "text": "\n4 ___ \u239b   \u239b    ___   ___\u239e                \u239b    ___   ___\u239e              \u239b    ___\n\u2572\u2571 a \u22c5\u239dsin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4) + sinh\u239d2\u22c5\u2572\u2571 a \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                          _____________       \n                                                 4 ___   \u2571   ___   ___        \n                                               8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\n\n   ___\u239e                 \u239b    ___   ___\u239e       \u239e\n\u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                               \n                                               \n                                               "
      }
     ],
     "prompt_number": 278
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
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       "prompt_number": 279,
       "text": "\n4 ___ \u239b   \u239b    ___   ___\u239e                \u239b    ___   ___\u239e              \u239b    ___\n\u2572\u2571 a \u22c5\u239dsin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4) + sinh\u239d2\u22c5\u2572\u2571 a \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                          _____________       \n                                                 4 ___   \u2571   ___   ___        \n                                               8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\n\n   ___\u239e                 \u239b    ___   ___\u239e       \u239e\n\u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                               \n                                               \n                                               "
      }
     ],
     "prompt_number": 279
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 280,
       "text": "\n4 ___    \u239b    ___   ___\u239e           4 ___    \u239b    ___   ___\u239e   4 ___     \u239b    _\n\u2572\u2571 a \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4)   \u2572\u2571 a \u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \u2572\u2571 a \u22c5sinh\u239d2\u22c5\u2572\u2571 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n           _____________                      _____________               ____\n  4 ___   \u2571   ___   ___              4 ___   \u2571   ___   ___       4 ___   \u2571   _\n8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)    2\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w      8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 \n\n__   ___\u239e           4 ___     \u239b    ___   ___\u239e\na \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4)   \u2572\u2571 a \u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n_________                       _____________\n__   ___               4 ___   \u2571   ___   ___ \na \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)     2\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  "
      }
     ],
     "prompt_number": 280
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAv4AAAAzBAMAAAAdohHJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 281,
       "text": "\n4 ___ \u239b   \u239b    ___   ___\u239e                \u239b    ___   ___\u239e              \u239b    ___\n\u2572\u2571 a \u22c5\u239dsin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4) + sinh\u239d2\u22c5\u2572\u2571 a \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                          _____________       \n                                                 4 ___   \u2571   ___   ___        \n                                               8\u22c5\u2572\u2571 w \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\n\n   ___\u239e                 \u239b    ___   ___\u239e       \u239e\n\u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                               \n                                               \n                                               "
      }
     ],
     "prompt_number": 281
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)",
     "language": "python",
     "outputs": [],
     "prompt_number": 282
    },
    {
     "cell_type": "markdown",
     "source": "68"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(1/sqrt(t))**3*cos(a/t)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADgAAAAuBAMAAACPJ8erAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nN4sZQGpVn49XvAdMcXZpYhAMTgAAAABJRU5ErkJggg==\n",
       "prompt_number": 283,
       "text": "\n   \u239ba\u239e\ncos\u239c\u2500\u239f\n   \u239dt\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\n  3/2 \n t    "
      }
     ],
     "prompt_number": 283
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAwIAAAAzBAMAAADWXKIeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
       "prompt_number": 284,
       "text": "\n4 ___ \u239b   \u239b    ___   ___\u239e                \u239b    ___   ___\u239e              \u239b    ___\n\u2572\u2571 w \u22c5\u239dsin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4) + sinh\u239d2\u22c5\u2572\u2571 a \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                          _____________       \n                                                 4 ___   \u2571   ___   ___        \n                                               8\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\n\n   ___\u239e                 \u239b    ___   ___\u239e       \u239e\n\u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                               \n                                               \n                                               "
      }
     ],
     "prompt_number": 284
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAtoAAAAzBAMAAABbFLJjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 285,
       "text": "\n4 ___    \u239b    ___   ___\u239e           4 ___    \u239b    ___   ___\u239e   4 ___     \u239b    _\n\u2572\u2571 w \u22c5sin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4)   \u2572\u2571 w \u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0   \u2572\u2571 w \u22c5sinh\u239d2\u22c5\u2572\u2571 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n           _____________                      _____________               ____\n  4 ___   \u2571   ___   ___              4 ___   \u2571   ___   ___       4 ___   \u2571   _\n8\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)    2\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w      8\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 \n\n__   ___\u239e           4 ___     \u239b    ___   ___\u239e\na \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4)   \u2572\u2571 w \u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n_________                       _____________\n__   ___               4 ___   \u2571   ___   ___ \na \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)     2\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  "
      }
     ],
     "prompt_number": 285
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "combsimp(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAwIAAAAzBAMAAADWXKIeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
       "prompt_number": 286,
       "text": "\n4 ___ \u239b   \u239b    ___   ___\u239e                \u239b    ___   ___\u239e              \u239b    ___\n\u2572\u2571 w \u22c5\u239dsin\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cos\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4) + sinh\u239d2\u22c5\u2572\u2571 a \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                          _____________       \n                                                 4 ___   \u2571   ___   ___        \n                                               8\u22c5\u2572\u2571 a \u22c5\u2572\u2571  \u2572\u2571 a \u22c5\u2572\u2571 w  \u22c5\u0393(3/4)\n\n   ___\u239e                 \u239b    ___   ___\u239e       \u239e\n\u22c5\u2572\u2571 w \u23a0\u22c5\u0393(-1/4) + 4\u22c5cosh\u239d2\u22c5\u2572\u2571 a \u22c5\u2572\u2571 w \u23a0\u22c5\u0393(3/4)\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                               \n                                               \n                                               "
      }
     ],
     "prompt_number": 286
    },
    {
     "cell_type": "markdown",
     "source": "69"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(t)*sin(a*sqrt(t))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAAuBAMAAAB9m5IOAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 287,
       "text": "\n   \u239b    ___\u239e\nsin\u239da\u22c5\u2572\u2571 t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     ___    \n   \u2572\u2571 t     "
      }
     ],
     "prompt_number": 287
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAA3BAMAAABeLN0NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVLvvZjKrRBAiic2Z\n3XYWw4KHAAAEZ0lEQVRYCd2WXYjcVBTH/9nNZLI7X1lFELS6sAhFsYoUWj+Q8aNLQbCBwjzow86b\n1ofugC+yKl5a+9AXJyIurVp28EXxQVet9GGR9qEVQbsdC0ULRSKuLy3aad2lrV/xnJubzCQzYZ1k\nnzww956Pm9+c3HuSHCBRPO9KYiwSqHieFXGsY1w7fGidFSo8dvjIUODr/w3LqwpZwWN27595nne9\nIR2ZwfO9XGwm66eNATMqlNwJUkcE21kzLrtMCWTEIS1XZzMd+AnB17KUhJzUUANv+Xm20oFvE4qE\nmwJFznsw0gIusp4OLClyeKGrAmN1VKgmXmRfVvD3vWDDxgzZTZEKrE88lbvXfvnGk8vMvEG/8som\nVoF5vPIleUe5kofPeA6GaNrmP1gQdPP8LG7BaYYCp1inA63SMDz41UYeFRurPCDXAfQ2vkX+sgVz\nElhjppsKbHh3MXNNnhODR1v4jh6LRYzb8o/SgsWbs04I5q1YaJg05tewj7KnpFGyUmW8A+NuCDbp\n8GaE3ibUWXwAGK6W+vCmUW4Q+JrcCmwjjvNu3QXuPETZFqydQMVJlfHTKyu52WO1P2+ZPUrXUxXk\nT+7cS6jR5QagLdvAbvKHVVFlg0SXoza1leZn8lM/snnp9+elF+h/0U+rCFXz1UCVPlVuBmfPYp6g\nIffcwT9oZevjA8ddoGa/R5aUfvB+FaErw8/hF+xT4MfC+B2kPQuT6nFZr6PZBp/Pqgr3g4tWeCVt\ngpRcmycFlrp0FwTwIPRFqpzdAkYHOtEcGRq0FZhUoe5UlP/ggzU39JerKE5CE9jf2AGMd6BdFWGw\nP2PMhcFA8T0+2GgEXuQW0ZTWr+wq3g+c4YP0ZQBYk/kFC2g2XWn44Aod2LQot0qE7GCXjHzGY6FO\nkePnpIOGAeAgFJ99cJNuumSVqvz62M7vKpJHeKD3toDmCRxga3jwW8BLTdF0NMr4PO6RkAd4fB9G\nFdhl4aT0ccbUOqwvQVUcoQsu4WboAjiH+8iy8TmN5g/4maYZx/9ADp8xl/lRfCWfu+34xELRxeUW\nsM/BGTqcjzD3KN1Liq2gw6MX7Ba8TnMHC1cO0gem9Jf9xtfAa1vFOy60OkVSgAuU1jbzIbhUA5NU\nBhccopz++xSN+amHP6Syq5KaDJ6hXZcLuoNfFdzP1C7O/0Y8vdoNdrWSLdhIKrfN3ZWB5oPNdmCj\nIEK1R6nk6Z4SwbJl61nNqg/ml7+S/keUA0X/LZWQMbVsbwfXB7MCG0I5zHoQGTQngGvA3fHlCmy6\nKlAW8RW9dgJ4D+hLFRMFjnmTzMFgatm4DYjKRoANO//NBTfKDQ4v5k0yB2dM3dVInJsZrFq2iqzG\n3nwybkXQsnH3GpWMYNWy4fEolaysYL9lw15YMXRWsN+y4VNdbDRYtmy4/ZcYN/NW+C1bnEp25q3o\ntmxRemZwt2XbYDB9dgdK5owHUsn5fwevTtyadOtRvzaxKf4oRhfErKWlYzFPgllYWmr0hf4FojVK\nN/V9F4gAAAAASUVORK5CYII=\n",
       "prompt_number": 288,
       "text": "\n               \u239b   \u239b    ___\u239e      \u239e\n               \u239csin\u239da\u22c5\u2572\u2571 t \u23a0      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c     ___          \u239f\n               \u239d   \u2572\u2571 t           \u23a0"
      }
     ],
     "prompt_number": 288
    },
    {
     "cell_type": "markdown",
     "source": "70"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-b*t)*sin(a*sqrt(t))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG4AAAAhBAMAAADKe4NxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n9SS6SOAfs62Ievoepw0AAAAASUVORK5CYII=\n",
       "prompt_number": 289,
       "text": "\n -b\u22c5t    \u239b    ___\u239e\n\u212f    \u22c5sin\u239da\u22c5\u2572\u2571 t \u23a0"
      }
     ],
     "prompt_number": 289
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception",
     "language": "python",
     "outputs": [],
     "prompt_number": 290
    },
    {
     "cell_type": "markdown",
     "source": "71"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(a*sqrt(t))/t",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAApBAMAAABgnqK2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 291,
       "text": "\n   \u239b    ___\u239e\nsin\u239da\u22c5\u2572\u2571 t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     t      "
      }
     ],
     "prompt_number": 291
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAA3BAMAAABeLN0NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n4n7lFgAAAABJRU5ErkJggg==\n",
       "prompt_number": 292,
       "text": "\n               \u239b   \u239b    ___\u239e      \u239e\n               \u239csin\u239da\u22c5\u2572\u2571 t \u23a0      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239d     t            \u23a0"
      }
     ],
     "prompt_number": 292
    },
    {
     "cell_type": "markdown",
     "source": "72"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "1/sqrt(t)*cos(a*sqrt(t))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEwAAAAuBAMAAABwheJJAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nd8cJo1T0H49SnlQBmweYAAAAAElFTkSuQmCC\n",
       "prompt_number": 293,
       "text": "\n   \u239b    ___\u239e\ncos\u239da\u22c5\u2572\u2571 t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n     ___    \n   \u2572\u2571 t     "
      }
     ],
     "prompt_number": 293
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALIAAAA3BAMAAABa2Q0wAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
       "prompt_number": 294,
       "text": "\n               \u239b   \u239b    ___\u239e      \u239e\n               \u239ccos\u239da\u22c5\u2572\u2571 t \u23a0      \u239f\nCosineTransform\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500, t, w\u239f\n               \u239c     ___          \u239f\n               \u239d   \u2572\u2571 t           \u23a0"
      }
     ],
     "prompt_number": 294
    },
    {
     "cell_type": "markdown",
     "source": "73"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*t)/sqrt(t)*cos(b*sqrt(t))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG4AAAAuBAMAAAA7LTGkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nZI9yZbpfI8X4N/cXS0vFQtsh/GsAAAAASUVORK5CYII=\n",
       "prompt_number": 295,
       "text": "\n -a\u22c5t    \u239b    ___\u239e\n\u212f    \u22c5cos\u239db\u22c5\u2572\u2571 t \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n        ___       \n      \u2572\u2571 t        "
      }
     ],
     "prompt_number": 295
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#cosine_transform(_, t, w)\n# Python exception",
     "language": "python",
     "outputs": [],
     "prompt_number": 296
    },
    {
     "cell_type": "markdown",
     "source": "74"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*sqrt(t))*cos(a*sqrt(t))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH0AAAAhBAMAAAAG4rmaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n6YGS2Zb4C9ODgBd678X/AAAAAElFTkSuQmCC\n",
       "prompt_number": 297,
       "text": "\n      ___             \n -a\u22c5\u2572\u2571 t     \u239b    ___\u239e\n\u212f        \u22c5cos\u239da\u22c5\u2572\u2571 t \u23a0"
      }
     ],
     "prompt_number": 297
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOoAAAA5BAMAAADKEKr8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 298,
       "text": "\n  \u239b      \u239b  2\u239e       \u239b  2\u239e\u239e\n  \u239c      \u239c a \u239f       \u239c a \u239f\u239f\na\u22c5\u239c- sinh\u239c\u2500\u2500\u2500\u239f + cosh\u239c\u2500\u2500\u2500\u239f\u239f\n  \u239d      \u239d2\u22c5w\u23a0       \u239d2\u22c5w\u23a0\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n              3/2          \n           2\u22c5w             "
      }
     ],
     "prompt_number": 298
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOoAAAA5BAMAAADKEKr8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 299,
       "text": "\n  \u239b      \u239b  2\u239e       \u239b  2\u239e\u239e\n  \u239c      \u239c a \u239f       \u239c a \u239f\u239f\na\u22c5\u239c- sinh\u239c\u2500\u2500\u2500\u239f + cosh\u239c\u2500\u2500\u2500\u239f\u239f\n  \u239d      \u239d2\u22c5w\u23a0       \u239d2\u22c5w\u23a0\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n              3/2          \n           2\u22c5w             "
      }
     ],
     "prompt_number": 299
    },
    {
     "cell_type": "markdown",
     "source": "75"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "exp(-a*sqrt(t))/sqrt(t)*(cos(a*sqrt(t))-sin(a*sqrt(t)))",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP0AAAAyBAMAAABlpcCuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIjKruxB23VSJRO9m\nmc3kD4mRAAAEm0lEQVRYCeVYXWgcVRT+ZnZnfya7zdqoKIIZyIMPIll9CPiUVVOlIGVFEUFKVh+i\nhsWuUkFEYaiCvqhR8UURBh+UotXom4IQrE1Fi8Sia8GNFAUV8SEbTCmhuH7nzv/OJn0QvGAP7Jlz\nvnu++e69c+cydwFtZo8PBhva1IGDGrVF+pVQf28YDF8NJ4kMBoMtLwlkY8NJYCYJ28wtjy5r1hos\nR2Cjnm30kYlUwz5mD6eQTJIi5JtAwd2RVK6huiJ3kLrRJoqRmWsMd65VdSnCDQIJMprEx1+sScmC\nuFFWaCXRvBSb9SQ0HKcJt0jzFH9DpMKCankd9puLUvKEuNi+boZxMYoEmYLhAI8x2tFSBKoajj/E\nNKlrbdgfw1oCnpU7lRriY3spUn0uBhndiDwpj/iY6abagiRFyNWEUCAnJKGyvr7eM7bMs9ZrqFKm\nJ7ycVIy0m5MoV+m4B7znY6WVZFsYpwhciyTYy2wMSH5ZqcM+zdeuZva4RVf0fDzrn0pCOQfTzOfZ\nbdpo/RThJgjB2opJigm7Xnwf1fr3zDbephuv+bj4ygvfmHc4H/RPdSXr81doPy8hMIFjvxEd81QW\n6Je6bZTabeEJLISFLzuqgvOlCJ8yU6RK+1vVgN7qGVjbS0x6Lt2kPyLVdhS55rxjnVOgIV2/HT+I\nNnBaYs7WCl00/kdxjfMWykvC40ZCQr5V7agdper4hKdZrUj7caUwA/sxUpVZDe1dz8a4gwviYG5w\nQjpYh33IhdUANlm2p0UX6lvncfCuPoy+8HzCSVTX8M554B4CQviVPyGVl+MNl9B9/Pkm+pfP0Ti8\n3OBWkd5US030x5bwJAd1FmVH9cfX/27uwOG52wCbAhVWXRCer/8Jii5wAHjVzyP98TvbNV9wyCfn\nv3nVbC3Sl+mc9GQBUYfDqTTIlLvTSiviQ/1zwlPzb2yrFfqhI/OlCOy+Ik16DEbZfKJbn6PcivQt\nLqfpZqXjAofxBienVRpaf5x/XLYJY1N4XOt9mFs4yapio+wFhHD9UUbetqyNeTF2HAWP+ttq/kHq\nWO3aegt4+YoGn6J7InpbSiuK9BAqNW4la8IjQMJHxi8FTk9fHr8iyDshr1jexVcMs5Zvxdhqu23O\n/jH195HZPwlyQdi9EzMkj3U93rTrANf7xYF+aWYRlW4P5AlOwrFTdz/A6LNFOiGYywyEZPVWExNN\nILRKPYyGr8cjoPBXGAaY7YZA8hoTDjUCXN09xpPVQWxJD0fa/REqD9q3n8Ng1DUmzLtB+x6Hwa4k\nnAlKM5eqG0FOEJmdCBoRxAQzbL2Owe4k5MPazLWRQWRX28UambbTRC5CspcyrAA4mmnIIqmSTLO6\ndwZNcYAjQ3mUlpwo9AOrNQQMpRnCvSy4GGnoHpdYyo90jbZxic32/3C401w+Ooe1T6c4N/c1vfrq\nWKixC1PAXo3yPBZiv0Z9HnP4uajPcvzE07mJTsD+6ZmWnvEHx8LkB/R/2ZHwWMgDgx7Lq2Oh+ltA\nSwf8YyG+0CIuoupYiBm4mnqgjoX4vdLUpK+OhXjxQU3yiI+FenoQHwv16MP517r/AKvykC3gkkSZ\nAAAAAElFTkSuQmCC\n",
       "prompt_number": 300,
       "text": "\n                                      ___\n\u239b     \u239b    ___\u239e      \u239b    ___\u239e\u239e  -a\u22c5\u2572\u2571 t \n\u239d- sin\u239da\u22c5\u2572\u2571 t \u23a0 + cos\u239da\u22c5\u2572\u2571 t \u23a0\u23a0\u22c5\u212f        \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                    ___                  \n                  \u2572\u2571 t                   "
      }
     ],
     "prompt_number": 300
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "cosine_transform(_, t, w)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 301,
       "text": "\n      \u239b                            \u239b         \u2502    4 \u239e                         \n  ___ \u239c 3  5/2                 \u250c\u2500  \u239c   1     \u2502   a  \u239f    3  5/2               \n\u2572\u2571 2 \u22c5\u239ca \u22c5w   \u22c5\u0393(-3/4)\u22c5\u0393(7/4)\u22c5 \u251c\u2500  \u239c         \u2502 \u2500\u2500\u2500\u2500\u2500\u239f - a \u22c5w   \u22c5\u0393(-1/4)\u22c5\u0393(5/4)\n      \u239c                       1\u2575 2 \u239c5/4, 7/4 \u2502     2\u239f                         \n      \u239d                            \u239d         \u2502 16\u22c5w \u23a0                         \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                                                              \n                                                                              \n\n      \u239b         \u2502    4 \u239e                        \u239b  2\u239e                         \n  \u250c\u2500  \u239c   1     \u2502   a  \u239f       ___   ___  4     \u239c a \u239f                     ___ \n\u22c5 \u251c\u2500  \u239c         \u2502 \u2500\u2500\u2500\u2500\u2500\u239f - 8\u22c5\u2572\u2571 2 \u22c5\u2572\u2571 \u03c0 \u22c5w \u22c5sinh\u239c\u2500\u2500\u2500\u239f\u22c5\u0393(5/4)\u22c5\u0393(7/4) + 8\u22c5\u2572\u2571 2 \u22c5\n 1\u2575 2 \u239c5/4, 7/4 \u2502     2\u239f                        \u239d2\u22c5w\u23a0                         \n      \u239d         \u2502 16\u22c5w \u23a0                                                      \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n        ___  9/2                                                              \n   16\u22c5\u2572\u2571 \u03c0 \u22c5w   \u22c5\u0393(5/4)\u22c5\u0393(7/4)                                                \n\n             \u239b  2\u239e              \u239e\n  ___  4     \u239c a \u239f              \u239f\n\u2572\u2571 \u03c0 \u22c5w \u22c5cosh\u239c\u2500\u2500\u2500\u239f\u22c5\u0393(5/4)\u22c5\u0393(7/4)\u239f\n             \u239d2\u22c5w\u23a0              \u239f\n                                \u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                                 \n                                 "
      }
     ],
     "prompt_number": 301
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_)",
     "language": "python",
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMcAAAA6BAMAAAD2J1AyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIrt2ZlTNRImrEN0y\n75nBkDP4AAAE3ElEQVRYCd1YW4jcZBQ+mSSbmUzmIhRkQZ3piIpPxg7YC7hGtz4U6xppfaiXOkJF\n1AcHawUvsAP1QVBkECsoxY2uL32QLPiwPvgQ2qrMg3aLlUopMtIVWh9kVmqFZXE8579skmGSFiGL\n9EDP+f7znfN//yWThgVIt05Im3aI01A+Qs5HcCLMuYzSpxyMzcSyGHEbH+1Zxqhey8Iu8oZ5OI1A\nKPJUoi93GGXapSoCoZhYjYTR4mwP7kBgnuOjdP8qp61uro3oCy+9Gtki1aGZwObfxUfpflHQXslD\npHXTq5G9R1bkHULsAGQqIaotSbzFAJ1zup2V9GMM5PtynBxLYvOgu6zoveRSzhgDUWG43xFS5Fik\nx4VZmTxkMbmaHI/Gm0SiUCegNjfXhqssdYb5cU4JRPZ9FptbbhgOPYIlh3zENP74WHcFPFm0KV4w\n1zdwiefH+ONrIvklxbLty5pyVyIR9Rc4qAQ8+lWMyqrV4kOAhwT4RibCKETMFUrVvG8loy1INBKl\nyNOU1xfUjuTlge+ViTAKEZ3t+gnYJpn1e5UJGaXIvZQwusVXJOEHHCWLqEtU8RosOrwSTHmObPzg\n3tbxr42XNs3YUDmJDu0dRixP/8YiuorLkRDZ33Rgz7QD2AprOy8Ql18gX945JSoB/qKEMKMDH6Oq\nbyurUOmjQ/tQkjJWHI64iNpSzuNP521qhX/wIpAstHhF6C+HEIxFaMMa4DTCIdeI8AyW2AYBuIjv\nmr/XqlC7kVovAzvkXH2050dMKA0ybJ77M6D5A/ibO+Sep4ahNMTFDrpyo/Fio9EFmA0AHsEzdERr\nG8kJzENFtgxw8BX+k2Yq+1ZGRe6UpIzxnUiRHaKVRHIkEjPaiTQtgMOjIuzXazWPyho6TGbyuECp\nBVA7KVpJhL8kTmwPeCH66J3gO3kribTpuMihMZF5+N6jAZnv8shF1AW4P9+FP1gr6xIipm3xdwdW\nm9GnS2tOO70rb84927uym5yDBewRPkWawmoCcRHY12zDzJTDW5+cO4BV7BG2BnyR1KWw5Yr+cYH9\n4i3wq1PVntbHilMeLzvEwxjPf/GBuaL+anVnsMBiP4YxlTKFzyfZRf2Ye1jpInqYjdOcwt5dUO48\nfiRvT2KltpRWjlzJpQLcQ8l7DmyEH9E43X5iNO7h3ERbRVygxaVZoU/sQfBehoFeRXiGxun2CdGG\nbRr1CjyKsORQIsWMBSStHZuC/coSrYq/bFIakHqD6BOf7tb7N7PNs5dNast5ZGvDIb7wmncjVOup\n1YwsBbiY4XAAy9NN2vyWq7Zsj1esfyTE07GROnIH698isarooERrCe3qq8La02E9omvYvFaPdcT7\nY1Q4eCCEiEaWGePk4IgEFAtOdJSEC26U+SA6SMAT0fMauaGEFngmQozeUIQKoRm5RqUf5tPQsQh5\nSwRfF1D+T5lhHFwXB/V/3oQlbi/TNea8TKfnk/+wARqweQNErMiLJjO5QvSVmZXKJFi7PLUj/4yQ\njcxRyBfdojNhZzM9mxW/8V73Pb+qtzMSoY/IckB/DHkKNC8jkYP4gf4Zzn0ALoGWkQbA7QDv4uRr\ncCt8npnIbGDWcfKz5s/s4zAbnWI9T/fd2zbJPg6zEdFX6Eqytl+2Zq2A899X3wAR390AEeu/afwL\nhr2QjTtoUFMAAAAASUVORK5CYII=\n",
       "prompt_number": 302,
       "text": "\n      \u239b  2\u239e       \u239b  2\u239e\n      \u239c a \u239f       \u239c a \u239f\n- sinh\u239c\u2500\u2500\u2500\u239f + cosh\u239c\u2500\u2500\u2500\u239f\n      \u239d2\u22c5w\u23a0       \u239d2\u22c5w\u23a0\n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n           ___         \n         \u2572\u2571 w          "
      }
     ],
     "prompt_number": 302
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "#inverse_cosine_transform(_, w, t)\n# RuntimeError: maximum recursion depth exceeded while calling a Python object",
     "language": "python",
     "outputs": [],
     "prompt_number": 303
    }
   ]
  }
 ]
}