Basis_3F3.ipynb

{
 "metadata": {
  "name": "Basis_3F3"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%load_ext sympyprt",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from sympy import *",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "z = Symbol(\"z\")",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a = Symbol(\"a\")",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B0 = (a/(z*(a-1)**2)) * (1 - (-z)**(1-a) * (gamma(a) - uppergamma(a,-z)) - (a-1) * (EulerGamma + uppergamma(0,-z) + log(-z)) - exp(z))",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(B0)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
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       "prompt_number": 6,
       "text": "\n      2                  2                           2             -a         \n     a \u22c5log(-z)         a \u22c5E\u2081(-z)        EulerGamma\u22c5a      a\u22c5z\u22c5(-z)  \u22c5\u0393(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 - \n   2                  2                  2                  2                 \n  a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z   \n\n        -a                     z                                              \na\u22c5z\u22c5(-z)  \u22c5\u0393(a, -z)         a\u22c5\u212f             a\u22c5log(-z)           a\u22c5E\u2081(-z)      \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 +\n   2                   2                  2                  2                \n  a \u22c5z - 2\u22c5a\u22c5z + z    a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z  \n\n                                    \n   EulerGamma\u22c5a            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\n  2                  2              \n a \u22c5z - 2\u22c5a\u22c5z + z   a \u22c5z - 2\u22c5a\u22c5z + z"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "pf = a / (a**2*z - 2*a*z + z)\npf",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAAAiBAMAAACn2ErcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdmZU3buZ74kiRBAy\nzauYRQn6AAABX0lEQVQ4EWNgwAkYhUxwyuGTCGRIwSeNS47JgSENlxw+cfYGBmd88rjk5i/g/o1L\nDp/4+Q1MDgb4FOCQY58w94EADjl8wlxJ2g8n4FMwKjcYQuA/WeDDwDidR/ANWRZvZDi+gRyN5xn4\nF5Cjj4dhP0bSZ2oLJsKoDAw1kgznFVAFeQxQ+UAeUwKGUCEDXwGqILMCKh/IW8iAES4eDBxo5Quq\nPlDxyiM96QADXyHXARQDWQsYwGUvTAKmD8IHFa/z//9nYBBa2IiijWG/AAO47IVJwPSB+UyI4pVT\nAFVfGANUEioB08cA4iMVr4dA2qaGAkEgiMXYAJMES6SGxrqGxoEkGEB8RPHKZQAWhBOGDBsgkjAJ\nmH1gPqJ4NWZggusBMrgEGAQgkjAJmD4wH168cgVaPUbWd1RJMQAsCZeA6oPw4cXrRu4rCsj66v//\nDwBLwiWg+uB8ZNX42DB/gtQAAO4BiZVU9MyoAAAAAElFTkSuQmCC\n",
       "prompt_number": 7,
       "text": "\n       a        \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n 2              \na \u22c5z - 2\u22c5a\u22c5z + z"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(B0 / pf)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAASBAMAAACEMyQEAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ndRzbdgAAAABJRU5ErkJggg==\n",
       "prompt_number": 8,
       "text": "\n                                             -a              -a             z \n-a\u22c5log(-z) - a\u22c5E\u2081(-z) - EulerGamma\u22c5a + z\u22c5(-z)  \u22c5\u0393(a) - z\u22c5(-z)  \u22c5\u0393(a, -z) - \u212f  \n\n                                   \n+ log(-z) + E\u2081(-z) + EulerGamma + 1"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B1 = z*diff(B0, z)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(B1/pf)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAABJYAAAASBAMAAAD710mdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 10,
       "text": "\n    -a \u239b                     a  z         a                 a                a\n(-z)  \u22c5\u239da\u22c5z\u22c5\u0393(a, -z) + a\u22c5(-z) \u22c5\u212f  + a\u22c5(-z) \u22c5log(-z) + a\u22c5(-z) \u22c5E\u2081(-z) - a\u22c5(-z) \n\n                    a                    a               a                    \n + EulerGamma\u22c5a\u22c5(-z)  - z\u22c5\u0393(a + 1) - (-z) \u22c5log(-z) - (-z) \u22c5E\u2081(-z) - EulerGamma\n\n     a\u239e\n\u22c5(-z) \u23a0"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvkAAAASBAMAAAAzjtwjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
       "prompt_number": 11,
       "text": "\n        -a               z                                                   -\na\u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + a\u22c5\u212f  + a\u22c5log(-z) + a\u22c5E\u2081(-z) - a + EulerGamma\u22c5a - z\u22c5(-z) \n\na                                         \n \u22c5\u0393(a + 1) - log(-z) - E\u2081(-z) - EulerGamma"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAAASBAMAAADPm/fpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\noNkpXhyHEWXawh+7/gf/ahY6G0CGZwAAAABJRU5ErkJggg==\n",
       "prompt_number": 12,
       "text": "\n          -a                -a               z                                \n- a\u22c5z\u22c5(-z)  \u22c5\u0393(a) + a\u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + a\u22c5\u212f  + a\u22c5log(-z) + a\u22c5E\u2081(-z) - a + Eu\n\n                                          \nlerGamma\u22c5a - log(-z) - E\u2081(-z) - EulerGamma"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B2 = z*diff(B1, z)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(B2/pf)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAABWUAAAAXBAMAAACR7zB0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZqsiVN12RBDvzTKJ\nu5m05BpfAAALXElEQVRoBe1ab4hcVxU/uzM7O7uzOztr223FEhcU20Kxg9WCiu6IbfxSYUUxH1R8\na+oqmJRtlaD4h0dLC1ZwA4VaUIhIgwU/OIIGbWkzKlTE2k1NCVa6mmj8EyFLrMbmS13Pufec++45\n792ZzYfm017IvHvP+d3fOed3z7x5sxOAyxrHPtW/LPwueFeBK69ALW7SZtZ69MqnsBtxVwFRoLnm\nZh1Z0zUsGqsnnf1tsbd1AV6J1wBjesmramsMDXFiYxFdWd1CUdJCEixD2aJ2OOrVg90SWiWitwSs\nMidiK8ywQrSPwlelJbFVepXg0QjhModVyYZYVYlaEJEy0KLiHEoY2hiGSjjB4MCVwLvINd4NbDj5\npiz+1rzgpr8Xg7v2m/9Wa3iTXvKqebrSXBh10GAP0YMlTFQg4pcEAdrfvj/AoonaQYW1s3V0vzuC\n2OoTeSsmHTuQKUwhY/CHiS49pBX8ajIaPAxx7qfqbM1hhdBaEY0qKaLq3IkWlkEnnGAgEaqBszm6\nriZ/GPUMxra2ts7ULrW+S8ZGRq/FaA/c/OkjN//ikzm+63puWXrZW7I4g2wzQZ2veQMARo/H9ed7\nsjSB9oIkiIC339YXWHQ1O5B6KX8CoPUnBdbVQ2Xehklit869/OyfL3JEgzGFRGmZ0iWtCDH23Ath\npdOrAA+jq73/c4GIJuUcqxQxKKNIyevPAQ/2uVuWOVoJo7LQJaHi0UnuANhaRJBEYvzj/lpfbgxo\nNpHTazH28HQjh3E8/InCo2bTuVu2esoKwNtU0B976DP/wStH97sa3da/ZL8JNJ1LggIoXc0OpL4D\nDiBqDtMuhqme8y78NDNMIfbMJYAHGGowuhBFZyJKWohhtfbD8Y7sGAlWSuKuiE44ALzCto6A1YqY\nSsxJlrx8DniwTUm2hCkywZmg2BjUDPULOgH8cOnWBit+y+TixD00+6AwsDlr+gnmSBKbd2EANzpu\nWveXYKaepW3qNvQ+dlPPcnRvmcrgJvbZQI2OJOgAucCiq01tBe6FfZiPOiGVCG7mvCManBqmEJt6\ndqzrsQajC4npbERJCzGs1iMwfph3jAYPQSAHHxYrXM6xQpFytS4XOUnDEbTAg4WrOOsShu2eKItX\npHg4SYnhAbYyAeJ9Z3xNc+DHpxtnFs7S9Wa/ktdj97/BTynHDOAGcZirf7CQUyicvE0FjXtWorsd\nEwPqcT9MIOTnBNF97POnGRVfzA54Atrzd/dMz6pEcDfnHfOUigyxsWe/2Op7bDma5ggrG1HSQgCf\n2ceB3gxujAYPQUDrM+/1NKxwOccKReyRmpM0HEGLjXwyf5KzLmPYQRebcGAI9TM4BfwSHmHBN/7I\nZD9ek2df4V69erm2vX0B4Kbsy9JMuAK0FyCckRvIUWTRWLkDs0V67kEK6mwEins2yoZc8KLQez5n\ni/hxvbDn1u7RvnPIi0/I7hBqvM/uXehAe/Xn+I4VI23VvI6smkmYsbX+ITHFJjwxMcC5ffh92xcc\nOaze4T4ze3jH4CTd2Mpfbp3+mE+PFU7lqBThk3MbI0UkN8sh6428nftgcvaWgb1RwlZxieHUio/G\nCSWJreewLpHwg/nQMwBTeWHAWfFngtmsvexcjWsPZNyz9LeFYOd9zg2PupVkcQr+6um5ZymosxEq\n7lkTvflfpuc/YhA85sfog1qGxnj4hEo7hHquP3ManoW3wlYL4uo1ryNMMPnaAGb+90+5ISajeZ6z\nn4YnueAheotasJ7tGJykewluC6J4hZM5KkVKKHWSCS9+Udn6Yc7xkhjnjxK2inP9s06t+GhcY3JL\nwdQavDNUBlDL8AtHNzLgd7qwugbap3mBavjmqx0GiOyFG/BJGQdnMbYMW7iqSatTULahOe5ZHR1m\nTzM9BQqDDsPzA/waZlTC6PIJlXYI9Vx/qQtL3Y/C6xEbV+8OWXhdsASTYPA+eyPiTuK/ZDTHcztM\ndgZccByxlim9WS2AP4o6o8EpxMxh+KWLTS9e4WSOSpESylfLuSW81A/jOUaq1EL0olSGKc4xnFoa\nWMtwJ9NMdOAdKPgmDTT/CD0TfXwJA39EgPeQ9xR8ByZ63t7qhJ5dhsLOOCA30KfS+c0/fGLzdziZ\nGsBH8IL0vtUpKNvam5tHNzcX0Qv0HYyih3SAvuf7sDUMVOKnTa8uXEUXHOJO7ZDC5vpvxGeCzkH3\nqI6JhI0h71FM/IlLj53XQe/Oh5GjlJ8qBIva3+GCk3oHtaAxEHVGg1OIuedXupgXjqBwZY6EUIqU\nUOokK73EsZGP5XWo1oIYgqaVihNDqN+pBaXGdC2FuOkMvk54PyZ7eJWPUG+invWj9gqs5376Bbz4\n5msehsjuvUBu/WywtNbE+zXRc89iUG8jaHyf1dHrWZPpMVAYET9FtyO1Q6j9CWX3rPZwZ1R9nLfn\nTDH5T0t8NqAPoQFQz5byk2ieCZ/Kcy44imj1lvvsXtg5OEW3tCaR8crPBlZDyVEpUqrEV8u5Jbz+\nYGegWgvRy2UUJWwVl/pJLXU0Tih5NpjO4kfd2+mHubmoVrx/0LG40boE19TdrN6DjjTfBSjsDHRu\n8L3OWRzPx5Z7QPTcsxjE22hP3LM6+iFoCL3nI3jMD/SzXE7WYqR2CDV+EvZhqT9wO8SIC8XrnCkm\nyYV6tpW5c+J6aZvniYgd1wEpOHJYvVmtyQwyVmc0OIVY78ofujA8Kyx52xyVIqVK1EkmvL5nj/me\nTWKcEFHCVvGiZ/HzNW5EJ5TQ4qf9dN9R4cvkqQ+8GeApWbpr9FPtw7XvNZztq3fd25Pm+wGmSfaf\nBBZw7tYJB+UsprrvWswcPfcsBnU2B4p7VkVvPT9/0NMDYCAeMT/ACzC2Jh6+cqJmRygMv3Es4uP1\nSk7wonqV91Amrs3fZx9a8z2bisZM8BspuIhY0pvVemp+4QSrMxqcQsz24FqJLT2bylEpklBa+slw\nBC028DeF73PPpjAunyLhkuISA1Ct+Gi8UBIKv4M1MintwebRDsC8LP31W2H5tfn79tOimT30IXj6\nyEuuS1cBnP34QHDODWPIhIOzmDxz3Vu6RC/bMKizOZDv2dpvL/7dRJ/a3n7V0+OnhYPii+LH/x8x\n75ISL105UbNDCmvd8hjsubsD69sXM/wjBP7zw/A6YzUT1wb02+35I13fs4lowg4DKbiIWNKb1Tqy\nvX2C1RkNTiGaZxa6ITjfFRI5akUSSks/GQ7Rgn67fRE/8+g5KcHA2RQJlxSXGPTAFR+NF0pCzeEn\nyDKT8eVxvTyll3b1gBh8j8oKpnM3newFi5qooO75lN0merEpBPIm5i/85ZnZYX5NrZ2EbzyG7wBT\nfSWvYbIYd04GY6L5U3A52ohRxZM9W8Vo8BBEQcYKD8+RFQm/RvN2c5KGYydaaIxNOPIW9Q8weAr4\nM/T9ipPzl8mBWsLr9NKuZtbYYnr2KxZo1jpocNrowQEhkDeN4keU2WGo64sAZxFlEqnkNUwW43rW\nYEw0aA4wlh86ogUKasfgy6AbnqMoYlCm2uFef58djtEJg+F3dXu1EkDqyPGc9XGX++IFzuOvecbl\nljd6Y72rnM1FtSwvdNDgt9GDA9xfQsNyJD8hOTXeZKnvXLm+hy6dSIJXMVnMoZfd+1VhwEary3vb\nRrRAzlYuOr0q8GiEcO1QEa2brXa4t0oLy6ATtl6XrFcrAaSn5WZWFAXw2XiB83bPGMzyQb+ua3Mj\n1+vSSgcNbhs9OAA4kLeM5CeY2lEqjKl1IglexbQTTClag8PhRUccUjFtGQ0ejShCqzpKOQpOoUrV\nDvd6jqEYnXCJnxgajqYa2Fr2MYa9nhjm3PXtKnCFFWj3Rweset4YvWsXsavAa6PATvqxvoO+fm2y\n22XdVaCkAD0w/B8xZuGH3HeMxgAAAABJRU5ErkJggg==\n",
       "prompt_number": 14,
       "text": "\n    -a \u239b   2                                     a  z         a               \n(-z)  \u22c5\u239d- a \u22c5z\u22c5\u0393(a, -z) + a\u22c5z\u22c5\u0393(a + 1) - 2\u22c5a\u22c5(-z) \u22c5\u212f  - a\u22c5(-z) \u22c5log(-z) - a\u22c5(-\n\n  a                           a           a       a  z       a               a\nz) \u22c5E\u2081(-z) - EulerGamma\u22c5a\u22c5(-z)  + 2\u22c5a\u22c5(-z)  + (-z) \u22c5\u212f  + (-z) \u22c5log(-z) + (-z) \n\n              a                  a\u239e\n\u22c5E\u2081(-z) - (-z)  + EulerGamma\u22c5(-z) \u23a0"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA18AAAAUBAMAAACAH5poAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nysELXtQc+gH3/9J/gq+tX5JmAAAAAElFTkSuQmCC\n",
       "prompt_number": 15,
       "text": "\n   2       -a                    -a                 z                         \n- a \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + a\u22c5z\u22c5(-z)  \u22c5\u0393(a + 1) - 2\u22c5a\u22c5\u212f  - a\u22c5log(-z) - a\u22c5E\u2081(-z) -\n\n                       z                                    \n EulerGamma\u22c5a + 2\u22c5a + \u212f  + log(-z) + E\u2081(-z) - 1 + EulerGamma"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAzoAAAAUBAMAAAC30VVcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
       "prompt_number": 16,
       "text": "\n 2       -a         2       -a                 z                              \na \u22c5z\u22c5(-z)  \u22c5\u0393(a) - a \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) - 2\u22c5a\u22c5\u212f  - a\u22c5log(-z) - a\u22c5E\u2081(-z) - Eule\n\n                  z                                    \nrGamma\u22c5a + 2\u22c5a + \u212f  + log(-z) + E\u2081(-z) - 1 + EulerGamma"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B3 = z*diff(B2, z)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(B3 / pf)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAABscAAAAXBAMAAACloIyZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZqsiVN12RBDvzTKJ\nu5m05BpfAAANe0lEQVR4Ae1afYhtVRVfM/fOvXfmzudTxyKxicQ0JG9ZQp9zo3z+YzBR5B99nVF5\nCfkxmgjRBwcloQxnQLLAQgklpT+6UT3K0nczKgT1PXsiGY7vPbKgwMfLKB+YTGvttdc+e+199rln\nHlH9cTfMPXvv9Vu/tdZv733Oufc9gHrtpj2DesAYtf+K/4VrnMd4ZqzA/6kCDT4hd7e3TjHBTtb9\n1n/f9RQjjt3GCvxnFehsGL5Fn9UNWvsOm/m3sbXXPuHDACb00I5KZrsn4GWHdfQ0Q2AJ4xB+R7ka\nQwk/zpfPFkzaTjnsu7ZXmFM95UaDymSJpZ5HJEJJAhGmJHYUrYTHTNUhc76KFcg1IZZircDtnhk9\nVBY0KKkfTHYJepxWCSY4IoyjKzoql10rchURTfYKOoA7ZPDnzgnT/b2dmFfpALxRgOraOaqGZjDo\n/F0mdSwCSxiAv/xUJRK6MkX9qBKSrtoLS5zPNq19/u5bfaTqK7fRyYaBCo93K9pYBGU2gxhTCOXQ\nUX7Ooju1yJyLYqX9UIjlMNTRrBpXtpa7WwaVxakpqRMsOPwqYoxvtX2Vy64VmcuR5nRF28xg4vjx\n48caJ7v3kqGV0SdA99HcXB+554JHP43dib4ZRh97oxlcpaFM6liwFyQMQOMDnxWUd7WuVVFv2QAk\n8tvEk0/7wzBXLHE1f8gi3n7xQGGXrshkHJQ4OtkwkHh0j6gYkQgS0LtGGBYKdXjywjWLi/Lz/GFi\n+Vw3TJA5u+oErEosBdSsCheu5Vkv9tG1ijlchgB7SkrqBN1mUxpGGFUiD4JcVKUWwRtOkwmuu4Ig\nWTPGwwN8ba61htSbyukTW9t+sTqYwyTumSmejT5ncjPV7XuWs10/iDWTSxiHCDriWhLVhvjF9X0A\nG9U6XwkHFn2eMNcH4BK4xgdQ/8dmYvZQ559iCdxKk1V1hqI4jwUUrGiRCMakmSKMFQp16Igtyq8I\nAfAEbGYyFgc7dmnhrbMvGHcNWHE/OLFYIkEGrB5OEHJt9bp/w34FsyDdNcC6lOsoKSRBgo7D1zDC\niLN3DXIpUcRuuIBMFPkIAB441dZ51F6ZuoF6H+JhcwtIJ2yYIi2NfnYYi/loLZpLky+m38461h7G\nai1KGAIIyoLp4lxLokqIhT4+b71wAHfB5JZHEuW6DjfC5c4jZ+j7zWV2Db4jrkGJpclKEuyT8lBb\nIxbBOCumGGOFQh3gNJtgFM3Om8uvYfqQHSfJcPGdCs43YAVPLJYowerhEKHWcjqD83GughmtOf4V\nLcA67esoaVmSZXsaxpgiBdcLcilRhDdcSCaK4P18csOxmY68Rx1bfoHGF7C1O+y8wj1KMQN4E4+i\nT37JVKu3/9bXWVgYC8E2DN5UP/O+iAyca0lU2SB0yGxUS/AJmD3pc4W5PgTzS9ehF7X9nztqriA7\nqHiSBW6lyUoSzJHyUFujRATyVkwlGBbqYN7Of87BwiXQGkDxJEuSBUFLawBPLJHIAENWDxeu5dSQ\nbs1hvj5zsQzJ2rj+OkpaijBBt36ehiUY6+1dglX187aK8IYLyUSRzwMsFHSTd7UH/pgsl+PfvtPX\nYO+ePhg7yYXtBP7RvN/Oz77AhmL1ENLY2UGwsYWxDAsxTKz/8aKZj/tcht24pqLKrqRD5ogsxdwW\ntNYvwTsIVeQbdRrLZ1/Uux8B1GQHzd8rhWHW0rzKdLKSBEuR8sCtsXd5Eeb3/RLvagkRFJOHYeWE\n+WA+n0tSModjlZ+1/xUf8KRBKiDBbND5b2zgj2aMDlm9VKxELKo3bybcuGwt4VkMlmT2l4GywhZi\nZVxHSWZIl+1p6JIu2Sr4W4KRxc9FV1psGsANFwUU8s0cNm1OeFm/+TcA03kxgT38YXAum18zc8bO\nh4x+enTz1qF15jUZAH91s6vnIGwLY1kwwHNwsSVxF+eaiiq70hwy+4VRvDczeAb+ZCuyP5OSjdOQ\nEueGjQwnudkdNPHm3BYWuUkMP1lVZ9JjYTB7FB6Ht8DxLj5hJKJNr0wxD+Orii/rx3+QW/9kNLbv\nwS/XRoNUQILZ9J/fu9YdMDpiFbEQbSUyCxKxOpwvD6eCb4/4RTfJrJaBPSKsaF9HSRvU05AzFg5P\nwyTGcLAsXi7RCZE7s3ltCMlEkekNeKcIgddGhl9Pe9hxrXES4AyYP8oTjcx8J8NBA09uMc9WMCcF\nv+Zhs6vnQegUhbGAwTC7Bb8ybt5H4drISqPaELDQRy9LhD3TnoeJNTiO3UbGuWKXG6UhJT4Gs0Wx\nolf3ZVsYlegauZUlq+pMecDCYLUHq72PwWuRJiGCYvIxnqqkw2SOHIfxLxkNbdQObFgNfLJGhpZC\nLA7a7MMNs1axiFXEQj+RyJCErIIrW0uYO1qSr3ioZcAw2KIsJOU6SjJFSmfRcI6WPizCkwb3sJFF\n59LIiu2D/qIIPF9CJvVNLcI7sKRtauj+Q4RODfDDNfznYPg2TPV5guz8JGusefPvJfdn8JvRItrp\npe/F7T98cvt32ClcjS2MZcAIW3hqvYcXasLluZZGdSH4kFFU5wqtIUwP4aM4R76Uq9hMGlLiq8un\noZna/Pb2/dvbK6b/oA0dudnXWS9ZlwTXmfLAQ/Z6LHLxWvMNt1SEgAkxOmV5lT6YT+RNuOxOtJdG\nkzrRPrNlNSgNSKVKUHy8tt5qFYtYRSxPIhI1uW8Kedy2AvNbbpK5WAbnEWGl/tFKOgWSZRsNm4/R\njivFCAPLYnR2iVHpJYq0hiVkgpvJ4Ktotq3dx4485HgOD1njZdjMzcjY+ZB1trx5hgLcRB1+KDfp\nvPkQYwtjyevi6gahVRsdlUPg5u2jo7wKMMdeyFc3OvgQNhljrq6ZNGyJGMJrfFOa7MOFP+KCIzcb\nQyWr6kx52EOW3bCvjwETIigmD+Oryre4WQA6ZMloaAM4ByZfYQ1SAQklGkLramB0xOrtB3vfNqJG\nrIJT8lAMbE36fTnFrJeBHSKsrC8fsmolmSJK0O0R2sGzME2HzNOZq5I4lgNlUXkbkFSKGHmS4YaL\nyQQ3k/lf1z5I/5llwfLzpXESuifhjKYZGTsfMjjhzVsPfLzi0TphRrx6hSvbPG7DZcGw2dO/+SJF\n4ZqKKhtkoY9wjmpC0w//kB3IJ9b6oKKgVaVB/xElty6i1+oKHLndFlxw+pXpZHWdCQ96XRzA6mBo\ngiVEUEweRsU27xH7+ZB5NWsMRWm8BHMnWQN/RSM9Fk1K+CQbgkWHNXip2C3FJN68mZBxyVrCzdDC\nOAlmvQw2nxAr4zpKWgpJCIe6bNrB+/mQJTGWozXEjsTGrqoUx3LbwQ2nTo7C4XvgzADBprWfufQc\ngIdlaK6kwJ2N75JGwHZ7yL5v53/i3OFLV93Yh+4h42dPgLiyLYplwTDXhzONm/chrqVRCecfMiFi\n/4eXlg9N9961krEvYK62mRRdiU/DxIZYrF6TeedfUnDgJjFUsrrOhAcestkV/Iq4nlO0UPAyxQqM\nUtU8yTrfs4csFc2UdB5sDo0GyYAEEw1hdoC7DhWDpFiI5i1lRS1S5AnZN0oeioE3zKeWrsVLkG/5\nMhiHCCva11LSUoQJOo6DOaCG5kmWxFgOlMXPRVeKJnvIaMPFOosi+MNHK7OEcFvn/kWAJRny9ZsA\nX1665UoaGPsj9zxHgWGfnT8wpBG1Tva1D+Pv20iBza6euLItimXB0Dm23DNu3oe4lkb1QrznyKc2\nJKp1v2dn51D72GvO7XFFlCs3m4aUeMeSqYttrFfnmicWpeDArTRZXWfCo3vhfXD2dYuwufOPDB8a\n+MeN0ytTrMAoVYH+S9CzdN8jgkQ0y/34U2A0SAYkXHHI8B5KikWs/n5giayoRYo8IaKWrOX0zs6r\ncb6OWS0DZ5+qrZaSliJMUNbPamgOWQpjKfCtEpvTOT4h9pDRhot1FkUW8D1tTRj5ir/8+g1/zyht\nX5HZRenwdSY313afh/ozjGXBGlQ1clER5IeoJvK9iD0okQOab2vctZ+BW2kMPwmAao/GYbj9PrwZ\nBYKXKZbAuPTMIauO5rCpgARw6ZvdZFwCVl8sJVGYYqmoRRLYq2BWOBoE2ED7aiUtWZhgwGEO2QgM\nH7Igl10r8jNM6Lc2Kb60h2oIe/TQjWY3bDc4ZF90iLKOjgXV4BICFzWwVRMFXmGJAZcbBm7VMYxX\ntUdzBeAFxNURYQTGHLLqaK6MWgG/7uABa1osnWIat3tm9AiyCLSvp6ROMNxs5pCNWgsjS5BLulId\n0OHoCE3mTgbs3OIPsO/9/qIt5/Gw2VPTnRU1DAc61ghw6ExjGzUwjSLSXmGJAVkxVG6jYhi3ao/L\n1s/qI6yOCNWYm18yt7bqaEUd1WQGd2mBVqzRfihwmrWOqHWZKYbCRtrXUlInGHC0r38DhanEALAs\nKpfdK0LfRTsZRZN2tXTsdb4fTMjwNu40ZczXVq7HwUjHGgEOfM3QRg1Mo4i0V1hiQFYMlduoGHF6\nKY86ItTBQN38apBliaohLZZmTeN2z0wetWrTKYR6V1s5rRGYzKBULrtWpLvGoao+D1UZx7axAmMF\nqhWYH1TbyRq8Do92GCPGCowVKBSoc4CaNQ5iwTjujRUYK+ArQC+k/wZQ1tk2B5d74QAAAABJRU5E\nrkJggg==\n",
       "prompt_number": 18,
       "text": "\n    -a \u239b 3               2       a  z    2                        a  z        \n(-z)  \u22c5\u239da \u22c5z\u22c5\u0393(a, -z) + a \u22c5z\u22c5(-z) \u22c5\u212f  - a \u22c5z\u22c5\u0393(a + 1) - 2\u22c5a\u22c5z\u22c5(-z) \u22c5\u212f  + 3\u22c5a\u22c5(\n\n   a  z         a                 a                  a                    a   \n-z) \u22c5\u212f  + a\u22c5(-z) \u22c5log(-z) + a\u22c5(-z) \u22c5E\u2081(-z) - 3\u22c5a\u22c5(-z)  + EulerGamma\u22c5a\u22c5(-z)  + \n\n      a  z         a  z       a               a                         a     \nz\u22c5(-z) \u22c5\u212f  - 2\u22c5(-z) \u22c5\u212f  - (-z) \u22c5log(-z) - (-z) \u22c5E\u2081(-z) - EulerGamma\u22c5(-z)  + 2\u22c5\n\n    a\u239e\n(-z) \u23a0"
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA/8AAAAUBAMAAAApR5C5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nD6n++X+RGYsZAAAAAElFTkSuQmCC\n",
       "prompt_number": 19,
       "text": "\n 3       -a             2    z    2       -a                   z        z     \na \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + a \u22c5z\u22c5\u212f  - a \u22c5z\u22c5(-z)  \u22c5\u0393(a + 1) - 2\u22c5a\u22c5z\u22c5\u212f  + 3\u22c5a\u22c5\u212f  + a\u22c5\n\n                                             z      z                         \nlog(-z) + a\u22c5E\u2081(-z) - 3\u22c5a + EulerGamma\u22c5a + z\u22c5\u212f  - 2\u22c5\u212f  - log(-z) - E\u2081(-z) - Eul\n\n           \nerGamma + 2"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA+0AAAAUBAMAAAAKHMFsAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
       "prompt_number": 20,
       "text": "\n   3       -a         3       -a             2    z          z        z       \n- a \u22c5z\u22c5(-z)  \u22c5\u0393(a) + a \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + a \u22c5z\u22c5\u212f  - 2\u22c5a\u22c5z\u22c5\u212f  + 3\u22c5a\u22c5\u212f  + a\u22c5lo\n\n                                           z      z                           \ng(-z) + a\u22c5E\u2081(-z) - 3\u22c5a + EulerGamma\u22c5a + z\u22c5\u212f  - 2\u22c5\u212f  - log(-z) - E\u2081(-z) - Euler\n\n         \nGamma + 2"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B4 = z*diff(B3, z)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(B4 / pf)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": 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       "prompt_number": 22,
       "text": "\n    -a \u239b   4               3       a  z    3               2  2     a  z      \n(-z)  \u22c5\u239d- a \u22c5z\u22c5\u0393(a, -z) - a \u22c5z\u22c5(-z) \u22c5\u212f  + a \u22c5z\u22c5\u0393(a + 1) + a \u22c5z \u22c5(-z) \u22c5\u212f  - 2\u22c5a\n\n  2     a  z             a  z           a  z         a                 a      \n\u22c5z \u22c5(-z) \u22c5\u212f  + 3\u22c5a\u22c5z\u22c5(-z) \u22c5\u212f  - 4\u22c5a\u22c5(-z) \u22c5\u212f  - a\u22c5(-z) \u22c5log(-z) - a\u22c5(-z) \u22c5E\u2081(-z\n\n                     a           a    2     a  z           a  z         a  z  \n) - EulerGamma\u22c5a\u22c5(-z)  + 4\u22c5a\u22c5(-z)  + z \u22c5(-z) \u22c5\u212f  - 2\u22c5z\u22c5(-z) \u22c5\u212f  + 3\u22c5(-z) \u22c5\u212f  +\n\n     a               a                a                  a\u239e\n (-z) \u22c5log(-z) + (-z) \u22c5E\u2081(-z) - 3\u22c5(-z)  + EulerGamma\u22c5(-z) \u23a0"
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAABMgAAAAUBAMAAACKUxx7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nwO+T/waSTKEVNFcQXQAAAABJRU5ErkJggg==\n",
       "prompt_number": 23,
       "text": "\n   4       -a             3    z    3       -a             2  2  z        2  z\n- a \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) - a \u22c5z\u22c5\u212f  + a \u22c5z\u22c5(-z)  \u22c5\u0393(a + 1) + a \u22c5z \u22c5\u212f  - 2\u22c5a\u22c5z \u22c5\u212f \n\n          z        z                                                2  z      \n + 3\u22c5a\u22c5z\u22c5\u212f  - 4\u22c5a\u22c5\u212f  - a\u22c5log(-z) - a\u22c5E\u2081(-z) - EulerGamma\u22c5a + 4\u22c5a + z \u22c5\u212f  - 2\u22c5z\n\n  z      z                                    \n\u22c5\u212f  + 3\u22c5\u212f  + log(-z) + E\u2081(-z) - 3 + EulerGamma"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "expand_func(_)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAABJwAAAAUCAMAAAD/XNdIAAAAM1BMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 24,
       "text": "\n 4       -a         4       -a             3    z    2  2  z        2  z      \na \u22c5z\u22c5(-z)  \u22c5\u0393(a) - a \u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) - a \u22c5z\u22c5\u212f  + a \u22c5z \u22c5\u212f  - 2\u22c5a\u22c5z \u22c5\u212f  + 3\u22c5a\n\n    z        z                                                2  z        z   \n\u22c5z\u22c5\u212f  - 4\u22c5a\u22c5\u212f  - a\u22c5log(-z) - a\u22c5E\u2081(-z) - EulerGamma\u22c5a + 4\u22c5a + z \u22c5\u212f  - 2\u22c5z\u22c5\u212f  + \n\n   z                                    \n3\u22c5\u212f  + log(-z) + E\u2081(-z) - 3 + EulerGamma"
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B5 = z*diff(B4, z)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Basis elemens",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b0 = simplify(z*diff(pf*log(-z), z) / pf)\nb0",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAASBAMAAACnV51MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 26,
       "text": "-log(-z) + 1"
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b1 = simplify(z*diff(pf*E1(-z), z) / pf)\nb1",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAASBAMAAACnV51MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIrt2ZpmJ70QQVDLN\n3atdH5w+AAABY0lEQVQ4EY1SPU/DMBS8lH44EQ0BBiQklnZAYgpSFyaKWhYmFvZKCJUtAyMDRfwB\nI1SxASNiiihM8ANgqOBHIAYWVCZG/Go7tqMKeIvv3t3F9ouBf1bT9jkEKB2e2qqDw8imfZsAi/Op\n3bg/et/7fFWdLVtBEDs0TxIOXwf1qjzPOS93uAhiQ3byWzQc4+B42+EJZ/xBdsKeo+DR0NbmbDRM\nDRco4SV9hBkjhAcsheGFjhcbUaJk50UHL43WONkFKlpAF+XIiCrIQ6EXqL9gabRDNcJcTVQdXy01\nBt0QzoQXeRB0KbgEeGSsidCd4NVUfcn7VsBeaKplVCh4bvrsSuDsqP4IEDa3KDiQQTMM3KAIazgr\nKPbcGB0V/pMMTqdaZPXrD+BWU/TbqxlWgJ7c8kgGp2KtnvnDJtDW9Jd1fMfs6Slj/slNyo+D2Hck\n1nHoRMLW36hPf9TUhYF/IT+7JDnXgB9NwkDtdD5eaAAAAABJRU5ErkJggg==\n",
       "prompt_number": 27,
       "text": "\n   z         \n- \u212f  - E\u2081(-z)"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b2 = simplify(z*diff(pf*EulerGamma, z) / pf)\nb2",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABcAAAAMBAMAAAB7FTvLAAAAKlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADmU0mKAAAADXRSTlMAIrt2me/dRGZUMokQfqDA4AAA\nAEpJREFUCB1jYIAAlrAChgYom0FlcgLXAiiHcwJDBTcDg5ASEChzMTAwS8BUAWlmG2TOBiQO9wJk\nDhKbAWgYApxGMBkYpiNzDBgYAC9uCE8hl/bxAAAAAElFTkSuQmCC\n",
       "prompt_number": 28,
       "text": "-EulerGamma"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b3 = expand(expand_func(simplify(z*diff(pf*( z*(-z)**(-a)*gamma(a) - z*(-z)**(-a)*uppergamma(a, -z) ), z) / pf)))\nb3",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWEAAAASBAMAAAB4EHI/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nX2TijpsEj6TIsU7HBdBPGahaWzdqSqL/7yTjNvHNs4cAAAAASUVORK5CYII=\n",
       "prompt_number": 29,
       "text": "\n          -a                -a               z\n- a\u22c5z\u22c5(-z)  \u22c5\u0393(a) + a\u22c5z\u22c5(-z)  \u22c5\u0393(a, -z) + z\u22c5\u212f "
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b4 = simplify(z*diff(pf*exp(z), z) / pf)\nb4",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEgAAAASBAMAAAAK1oXlAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAZqsiVN12RBDvzTKJ\nu5m05BpfAAABHUlEQVQoFW1Ru04CQRQ97iIO4gOCgc7W2JGoJHZ8AvzBEC0oKIjSGZONVlrgB1ib\nWG5lYWJCpaGgszWh8wPQUJl4zzIzO2y4yZ57XvvIDoASVs2yG9RXdTC07s7jLbBnVbrVAZDTRh83\nYqCVhoYV33+EPXu+u8PzwFLHGRGCvhMpYenVyJfLKXbJD/WVsRaLpSSo7h/Vn2I8iM7XenqRGmSp\nEAHbo1BD5pSARoIOWFqXXzPGliBwQiiWBMIvjqZOSjHwV61Q4o4wIHhjXhfOjcfvyzUzZ8OSBGoG\nROxtylOvzy+a5G5YepPrE2t9mnkNpe/bpHbCye83UBY5LJ8lpmrZLLP9Y8FHJjRyY+T7QeQrx28c\nI1F6SVrRtUT2P5wSNObVO7u+AAAAAElFTkSuQmCC\n",
       "prompt_number": 30,
       "text": "\n         z\n(z - 1)\u22c5\u212f "
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "b5 = simplify(z*diff(pf*1, z) / pf)\nb5",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAANBAMAAAC0vDhTAAAAJ1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAilU6eAAAADHRSTlMAIrt2EKtEMolU3ZnkUB5tAAAAKElE\nQVQIHWNggALXBBiLocJmApzNwEMGW0gJCJQZSNUrobMa4QigCwDk1wlyhdeXIQAAAABJRU5ErkJg\ngg==\n",
       "prompt_number": 31,
       "text": "-1"
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# \"Initial value\"",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Bb = Matrix([log(-z),\n             E1(-z),\n             EulerGamma,\n             z*(-z)**(-a)*gamma(a) - z*(-z)**(-a)*uppergamma(a, -z),\n             exp(z),\n             1])\n\nBb",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": "\n\u23a1             log(-z)             \u23a4\n\u23a2                                 \u23a5\n\u23a2             E\u2081(-z)              \u23a5\n\u23a2                                 \u23a5\n\u23a2           EulerGamma            \u23a5\n\u23a2                                 \u23a5\n\u23a2      -a              -a         \u23a5\n\u23a2z\u22c5(-z)  \u22c5\u0393(a) - z\u22c5(-z)  \u22c5\u0393(a, -z)\u23a5\n\u23a2                                 \u23a5\n\u23a2                z                \u23a5\n\u23a2               \u212f                 \u23a5\n\u23a2                                 \u23a5\n\u23a3                1                \u23a6"
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "B = simplify(pf*Bb)\nB",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 34,
       "text": "\n\u23a1        a\u22c5log(-z)         \u23a4\n\u23a2     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \u23a5\n\u23a2       \u239b 2          \u239e     \u23a5\n\u23a2     z\u22c5\u239da  - 2\u22c5a + 1\u23a0     \u23a5\n\u23a2                          \u23a5\n\u23a2         a\u22c5E\u2081(-z)         \u23a5\n\u23a2     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \u23a5\n\u23a2       \u239b 2          \u239e     \u23a5\n\u23a2     z\u22c5\u239da  - 2\u22c5a + 1\u23a0     \u23a5\n\u23a2                          \u23a5\n\u23a2       EulerGamma\u22c5a       \u23a5\n\u23a2     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \u23a5\n\u23a2       \u239b 2          \u239e     \u23a5\n\u23a2     z\u22c5\u239da  - 2\u22c5a + 1\u23a0     \u23a5\n\u23a2                          \u23a5\n\u23a2      -a                  \u23a5\n\u23a2a\u22c5(-z)  \u22c5(\u0393(a) - \u0393(a, -z))\u23a5\n\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n\u23a2                2         \u23a5\n\u23a2         (a - 1)          \u23a5\n\u23a2                          \u23a5\n\u23a2              z           \u23a5\n\u23a2           a\u22c5\u212f            \u23a5\n\u23a2     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \u23a5\n\u23a2       \u239b 2          \u239e     \u23a5\n\u23a2     z\u22c5\u239da  - 2\u22c5a + 1\u23a0     \u23a5\n\u23a2                          \u23a5\n\u23a2            a             \u23a5\n\u23a2     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500     \u23a5\n\u23a2       \u239b 2          \u239e     \u23a5\n\u23a3     z\u22c5\u239da  - 2\u22c5a + 1\u23a0     \u23a6"
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "C = Matrix([[1-a],[1-a],[1-a],[1],[-1],[1]])\nC",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 35,
       "text": "\n\u23a1-a + 1\u23a4\n\u23a2      \u23a5\n\u23a2-a + 1\u23a5\n\u23a2      \u23a5\n\u23a2-a + 1\u23a5\n\u23a2      \u23a5\n\u23a2  1   \u23a5\n\u23a2      \u23a5\n\u23a2  -1  \u23a5\n\u23a2      \u23a5\n\u23a3  1   \u23a6"
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(transpose(C)*B)[0,0]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA7cAAAAtBAMAAACHX4GIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
       "prompt_number": 36,
       "text": "\n      -a                                                                      \na\u22c5(-z)  \u22c5(\u0393(a) - \u0393(a, -z))   a\u22c5(-a + 1)\u22c5log(-z)   a\u22c5(-a + 1)\u22c5E\u2081(-z)   EulerGam\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\n                2               \u239b 2          \u239e       \u239b 2          \u239e        \u239b 2\n         (a - 1)              z\u22c5\u239da  - 2\u22c5a + 1\u23a0     z\u22c5\u239da  - 2\u22c5a + 1\u23a0      z\u22c5\u239da \n\n                         z                         \nma\u22c5a\u22c5(-a + 1)         a\u22c5\u212f                 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\n          \u239e       \u239b 2          \u239e     \u239b 2          \u239e\n - 2\u22c5a + 1\u23a0     z\u22c5\u239da  - 2\u22c5a + 1\u23a0   z\u22c5\u239da  - 2\u22c5a + 1\u23a0"
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(_ - B0)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 37,
       "text": "0"
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Derivatives of basis elements",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "M = Matrix([[-1,0,0,0,0,1],\n            [0,-1,0,0,-1,0],\n            [0,0,-1,0,0,0],\n            [0,0,0,-a,z,0],\n            [0,0,0,0,z-1,0],\n            [0,0,0,0,0,-1]])\nM",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 39,
       "text": "\n\u23a1-1  0   0   0     0    1 \u23a4\n\u23a2                         \u23a5\n\u23a20   -1  0   0    -1    0 \u23a5\n\u23a2                         \u23a5\n\u23a20   0   -1  0     0    0 \u23a5\n\u23a2                         \u23a5\n\u23a20   0   0   -a    z    0 \u23a5\n\u23a2                         \u23a5\n\u23a20   0   0   0   z - 1  0 \u23a5\n\u23a2                         \u23a5\n\u23a30   0   0   0     0    -1\u23a6"
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "e0 = Matrix([1,0,0,0,0,0])\ne1 = Matrix([0,1,0,0,0,0])\ne2 = Matrix([0,0,1,0,0,0])\ne3 = Matrix([0,0,0,1,0,0])\ne4 = Matrix([0,0,0,0,1,0])\ne5 = Matrix([0,0,0,0,0,1])",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e0) * (M*B))[0,0] - pf*b0)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 41,
       "text": "0"
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e1) * (M*B))[0,0] - pf*b1)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 42,
       "text": "0"
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e2) * (M*B))[0,0] - pf*b2)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 43,
       "text": "0"
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e3) * (M*B))[0,0] - pf*b3)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 44,
       "text": "0"
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e4) * (M*B))[0,0] - pf*b4)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 45,
       "text": "0"
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify((transpose(e5) * (M*B))[0,0] - pf*b5)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 46,
       "text": "0"
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**0 * B)[0,0] - B0)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 59,
       "text": "0"
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**1 *B)[0,0] - B1)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 60,
       "text": "0"
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**2 *B)[0,0] - B2)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 61,
       "text": "0"
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**3 *B)[0,0] - B3)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMBAMAAABCcoqQAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAVJlmiUTNuxAydkvU/DYAAABBSURBVAgd\nY2AQMhFgYGBNYChlYGAzYDBjYOgWYIhuYJgdwDB7AkP0BBADQkIYQFnpBgb2BSCVQF2pDAwMIlYC\nDADyLg3mxPBcdQAAAABJRU5ErkJggg==\n",
       "prompt_number": 62,
       "text": "0"
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**4 *B)[0,0] - B4)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAANBAMAAAA3eAFoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIrt2ZlTdme+JRBAy\nzat0m4fWAAAAgUlEQVQYGWNgQAPsPRvRRBgYRIUPYIhhF9iAIXx4YQFczNg1gYHB2V1Q4NoBmBiT\nAXsCA9MERgOYAJB2Y2AvYJjBwCkAEhNSAgJlhk4GtgCGT86OSMoYfzHs3wAkkAHPbwY3Vu6PDAwb\nkEQbGe8xM6gysCxAElvuss+QYbuLIUgIAJMPGTv5JJptAAAAAElFTkSuQmCC\n",
       "prompt_number": 63,
       "text": "\n    z\n-a\u22c5\u212f "
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Huh ??",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "simplify(expand_func(simplify((transpose(C)* M**5 *B)[0,0] - B5)))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAASBAMAAABvO3eaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 65,
       "text": "\n                 z\na\u22c5(a - 3\u22c5z + 3)\u22c5\u212f "
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}