{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{3}$}F\\left( \\left. \\begin{array}{c}1,\\;1\\\\2\\end{array} \\right |,z\\right)\\]"
      ],
      "text/plain": [
       "(%o3)                   hypergeometric([1, 1], [2], z)"
      ],
      "text/x-maxima": [
       "hypergeometric([1,1],[2],z)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SB-KERNEL:REDEFINITION-WITH-DEFUN: redefining MAXIMA::SIMP-HYPERGEOMETRIC in DEFUN\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{4}$}F\\left( \\left. \\begin{array}{c}1,\\;1\\\\2\\end{array} \\right |,z\\right)=-\\frac{\\log \\left(1-z\\right)}{z}\\]"
      ],
      "text/plain": [
       "                                                    log(1 - z)\n",
       "(%o4)            hypergeometric([1, 1], [2], z) = - ----------\n",
       "                                                        z"
      ],
      "text/x-maxima": [
       "hypergeometric([1,1],[2],z) = -log(1-z)/z"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assume(z<1)$assume(-1<z)$\n",
    "hypergeometric([1,1],[2],z);\n",
    "%=hypergeometric_simp(%);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{6}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;1\\\\\\frac{3}{2}\\end{array} \\right |,z^2\\right)\\]"
      ],
      "text/plain": [
       "                                        1       3    2\n",
       "(%o6)                   hypergeometric([-, 1], [-], z )\n",
       "                                        2       2"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1],[3/2],z^2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{7}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;1\\\\\\frac{3}{2}\\end{array} \\right |,z^2\\right)=\\frac{\\log \\left(\\frac{z+1}{1-z}\\right)}{2\\,z}\\]"
      ],
      "text/plain": [
       "                                                       z + 1\n",
       "                                                   log(-----)\n",
       "                                 1       3    2        1 - z\n",
       "(%o7)            hypergeometric([-, 1], [-], z ) = ----------\n",
       "                                 2       2            2 z"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1],[3/2],z^2) = log((z+1)/(1-z))/(2*z)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "assume(0<z)$\n",
    "hypergeometric([1/2,1],[3/2],z^2);\n",
    "%=hypergeometric_simp(%);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{8}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;1\\\\\\frac{3}{2}\\end{array} \\right |,-z^2\\right)\\]"
      ],
      "text/plain": [
       "                                       1       3      2\n",
       "(%o8)                  hypergeometric([-, 1], [-], - z )\n",
       "                                       2       2"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1],[3/2],-z^2)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{9}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;1\\\\\\frac{3}{2}\\end{array} \\right |,-z^2\\right)=\\frac{\\arctan z}{z}\\]"
      ],
      "text/plain": [
       "                                  1       3      2    atan(z)\n",
       "(%o9)             hypergeometric([-, 1], [-], - z ) = -------\n",
       "                                  2       2              z"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1],[3/2],-z^2) = atan(z)/z"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypergeometric([1/2,1],[3/2],-z^2);\n",
    "%=hypergeometric_simp(%);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{10}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;\\frac{1}{2}\\\\\\frac{3}{2}\\end{array} \\right |,z^2\\right)\\]"
      ],
      "text/plain": [
       "                                        1  1    3    2\n",
       "(%o10)                  hypergeometric([-, -], [-], z )\n",
       "                                        2  2    2"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1/2],[3/2],z^2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/latex": [
       "\\[\\tag{${\\it \\%o}_{11}$}F\\left( \\left. \\begin{array}{c}\\frac{1}{2},\\;\\frac{1}{2}\\\\\\frac{3}{2}\\end{array} \\right |,z^2\\right)=\\frac{\\arcsin z}{z}\\]"
      ],
      "text/plain": [
       "                                   1  1    3    2    asin(z)\n",
       "(%o11)             hypergeometric([-, -], [-], z ) = -------\n",
       "                                   2  2    2            z"
      ],
      "text/x-maxima": [
       "hypergeometric([1/2,1/2],[3/2],z^2) = asin(z)/z"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypergeometric([1/2,1/2],[3/2],z^2);\n",
    "%=hypergeometric_simp(%);"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Maxima",
   "language": "maxima",
   "name": "maxima"
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   "file_extension": ".mac",
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