Fourier_kukeiha.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = Symbol ('n', integer=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\left(\\int_{- \\pi}^{0} - \\sin{\\left (n x \\right )}\\, dx + \\int_{0}^{\\pi} \\sin{\\left (n x \\right )}\\, dx\\right) = \\frac{1}{\\sqrt{\\pi} n} \\left(- 2 \\left(-1\\right)^{n} + 2\\right)$$"
      ],
      "text/plain": [
       "0                 π                              \n",
       "⌠                 ⌠                              \n",
       "⎮  -sin(n⋅x) dx + ⎮ sin(n⋅x) dx                  \n",
       "⌡                 ⌡                 ⎛      n    ⎞\n",
       "-π                0               2⋅⎝- (-1)  + 1⎠\n",
       "─────────────────────────────── = ───────────────\n",
       "               √π                       √π⋅n     "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=(Integral(-1*sin(n*x),(x,-pi,0))+Integral(1*sin(n*x),(x,0,pi)))/sqrt(pi)\n",
    "Eq(a,simplify(a.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAABMCAMAAACbKHogAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{1}{\\sqrt{\\pi}} \\left(\\int_{- \\pi}^{0} - \\cos{\\left (n x \\right )}\\, dx + \\int_{0}^{\\pi} \\cos{\\left (n x \\right )}\\, dx\\right) = 0$$"
      ],
      "text/plain": [
       "0                 π                \n",
       "⌠                 ⌠                \n",
       "⎮  -cos(n⋅x) dx + ⎮ cos(n⋅x) dx    \n",
       "⌡                 ⌡                \n",
       "-π                0                \n",
       "─────────────────────────────── = 0\n",
       "               √π                  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b=(Integral(-1*cos(n*x),(x,-pi,0))+Integral(1*cos(n*x),(x,0,pi)))/sqrt(pi)\n",
    "Eq(b,simplify(b.doit()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAqBAMAAACzR/EDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n7hpk7gAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{2}{\\pi n} \\left(- \\left(-1\\right)^{n} + 1\\right) \\sin{\\left (n x \\right )}$$"
      ],
      "text/plain": [
       "  ⎛      n    ⎞         \n",
       "2⋅⎝- (-1)  + 1⎠⋅sin(n⋅x)\n",
       "────────────────────────\n",
       "          π⋅n           "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=simplify(a.doit())/sqrt(pi)*sin(n*x)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABeMAAAA9BAMAAADcw29iAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\sum_{n=1}^{20} \\frac{2}{\\pi n} \\left(- \\left(-1\\right)^{n} + 1\\right) \\sin{\\left (n x \\right )} = \\frac{4}{\\pi} \\sin{\\left (x \\right )} + \\frac{4}{3 \\pi} \\sin{\\left (3 x \\right )} + \\frac{4}{5 \\pi} \\sin{\\left (5 x \\right )} + \\frac{4}{7 \\pi} \\sin{\\left (7 x \\right )} + \\frac{4}{9 \\pi} \\sin{\\left (9 x \\right )} + \\frac{4}{11 \\pi} \\sin{\\left (11 x \\right )} + \\frac{4}{13 \\pi} \\sin{\\left (13 x \\right )} + \\frac{4}{15 \\pi} \\sin{\\left (15 x \\right )} + \\frac{4}{17 \\pi} \\sin{\\left (17 x \\right )} + \\frac{4}{19 \\pi} \\sin{\\left (19 x \\right )}$$"
      ],
      "text/plain": [
       "  20                                                                          \n",
       " ____                                                                         \n",
       " ╲                                                                            \n",
       "  ╲     ⎛      n    ⎞                                                         \n",
       "   ╲  2⋅⎝- (-1)  + 1⎠⋅sin(n⋅x)   4⋅sin(x)   4⋅sin(3⋅x)   4⋅sin(5⋅x)   4⋅sin(7⋅\n",
       "   ╱  ──────────────────────── = ──────── + ────────── + ────────── + ────────\n",
       "  ╱             π⋅n                 π          3⋅π          5⋅π          7⋅π  \n",
       " ╱                                                                            \n",
       " ‾‾‾‾                                                                         \n",
       "n = 1                                                                         \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "x)   4⋅sin(9⋅x)   4⋅sin(11⋅x)   4⋅sin(13⋅x)   4⋅sin(15⋅x)   4⋅sin(17⋅x)   4⋅si\n",
       "── + ────────── + ─────────── + ─────────── + ─────────── + ─────────── + ────\n",
       "        9⋅π           11⋅π          13⋅π          15⋅π          17⋅π          \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "       \n",
       "       \n",
       "       \n",
       "       \n",
       "n(19⋅x)\n",
       "───────\n",
       "19⋅π   \n",
       "       \n",
       "       \n",
       "       "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=Sum(c,(n,1,20))\n",
    "Eq(d,d.doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MwLPPPovo6Gj8/PPPGDdunMP+u3kceSGGlxw6BPToARTyFVM+4euvgcWLgRUr\neCGGXlq2BKZPB2JjzR5J4Ve+PHDxopcuxKD8YYWhH35at/4Yn/rxWguC8s/sCzGKEiZg/fFjifSh\nlBfXAVP+scLQDxOw/hif+khPl/cpyS8mYC9hgOvn9m15PEk/jE993G1sMgF7iZHX2xc3rID1xwSs\nj7uNTSZgLzHqevviiAlYf0zA+mAC9mFmX4xRVDAB648JWB9MwD6MQa4PJmD9MTb1wQTswxjk+khL\n4ySc3hibnvvpp5/Qp08TlCiRAU3TSmuatl/TtFzfDJkJ2IsY5Pq4fZsVsN4Ym55r3rw5YmO74cyZ\nNwDgLQCLlVIHc/sZJmAv4sUY+mALQn9MwPp48snxuHJlIwA0A/B2XrdnAvYiBrk+mID1x9jUx/nz\nF5GVdQMAygLIs1HGBOxFDHJ9MAHrj7GpjzlzXkJMzCQA+AysgH0Lg1wfTMD60/sTMYqjxYsXQ9MC\nERnZB5AecHNN0+Jy+5k8PxGD9MMErA9eiqw/xqbn+vXrhwsX+uHkSUApZQHQKq+fYQXsRbwQQx+s\ngPXHBKwPrgP2YQxyfTAB64+xqQ8mYB/GINcHE7D+GJv6YAL2YQxyfTAB64+xqQ++HaUP44UYnsvK\nAjIz5Z3lSD/8RAx9sAL2YcW5yrh8+TI6duyI+vXr49FHH8XVq1fd3s7f3x8xMTFo2rQpunfv7rLf\nWmFo+frIQ8qv4hybemIC9mHFOcinTZuG9u3b49dff0Xbtm0xdepUt7crXbo0du/ejT179mDFihUu\n+9l+MEZxjk09MQH7sOIc5CtXrkT//v0BAP3793ebXAHk+THzTMDGKM6xqScmYB9WnIP8999/R1hY\nGAAgPDwc58+fd3u79PR0PPDAA2jdujVWrlzpsp8J2BjFOTb1dLeTcLwSzouK+oUYHTp0QGpqava2\nUgqapmHSpEn5PsapU6cQHh6O48ePo23btrj//vtRq1at7P3OCTg+Pj7767i4OMTFxXnyKxRb1kuR\nlWJ/3RN3WyAwAXtRUa8yNm7cmOO+sLAwpKamIiwsDOfOnUPFihXd3i48PBwAUKtWLcTFxWHPnj0O\nCdi5wrBPwFRw/v5AQABw5w5XmHiCLQgfVtQTcG66du2KhQsXAgAWLVqEbt26udzmypUryMjIAABc\nuHABO3bsQMOGjh8owBaEcYpzfOqFCdiHFecAHzNmDDZu3Ij69etj06ZNGDt2LABg165dePHFFwEA\nhw4dQvNTzJvnAAAQe0lEQVTmzdG0aVO0a9cOr7/+Oho0aOBwHCZg4xTn+NQLWxA+rDhfiBEaGopN\nmza5fL9Zs2b46KOPAACtWrXCvn37cj0OE7BxmIA9xyvhfBgD3HNMwMZhfHqOLQgfxgD3HD8R2TiM\nT88oxQTs0xjgnuMnIhuH8emZjAxZSeLvn/+fYQL2Iga459iCMA4/lsgzBYlNJmAvKuoXYngDE7Bx\nWCB4piAflcUE7EUMcM8xARuH8ekZVsA+jgHuOU7CGYfx6RkmYB8XECAzpZmZZo+k8OIknHGYgD3D\nBOzjNK14X4yhB7YgjMNPxfAME3AhwCrDM0zAxmFseoaTcIUAg9wzTMDGYWx6hhVwIcAg9wwTsHEY\nm55hAi4EGOSe4SoI4zA2PcMEXAgwyD3DVRDGYWx6hgm4EODVcJ5hC8I4TMCe4SRcIcAg9wwTsHEY\nm55hBVwIMMg9wwRsHMamZ5iACwFeiOEZTsIZhwnYM0zAhQCD3DOchDMOY9MzTMCFAIO84LKy5GPT\nS5Y0eyRFU3AwX9w8wUm4QoAJuOCsAa5pZo+kaCpVCjh92uxRFF6sgAsBJuCC4wScscqWBW7cMHsU\nhRcTcCHABFxwTMDGKlsWuH7d7FEUXkzAhQAvxCg4roAwVpkyTMCeYAIuBO67T3ptzjIygNRU74/H\nF6WnA+fPu36fKyCMZa2AlXLdl5oqE6AEpKS4fyw4CVcIaBpw8qTr999/H+jbF9i/3/tj8jVTpgBP\nPw0cPer4fbYgjBUYKJ/a4twi+/FH4KmngFmzzBmXL9m+XZ6n8+e77mMFXAjcey9w9arj99LSgJ07\ngfbtgf/7P3PG5SvOnAH27gUeeQTYsMFxHxOw8dz1gdesAR59FNi2je2zefOAhx4C1q93PVNgAi4E\n7rkHuHbN8Xs//SSB362bvMIWZxs3AtWrA61aSeVljwnYeO4S8P79QKdO0iMuzvGpFLB1K/Dss/K5\njr/95rifCbgQcJeAf/kFqF0biIyUr921KH75Bfjzn4Gvv/bOOPX21VdfoXHjxvD398dzz+3GzJmA\nxeJ6uyVL1uGrrxpg6NB62Lr1LYfbcBLOeGXKOC5Fu3ZNqr3GjYGoKGD3btefuXMHmDwZGDcOuHXL\ne2M1wsKFwPDhwIkTrvuSkuR3bdAAqFlTztTsFSQ+mYC9zF0L4tgxoE4d6Q/36eNa+SkFfPghUL48\n8MUXwPHjrse9dQv46CNgz56c7/vCBeC773JeBqcU8OuvwJUrOR/j8GEgMdH9RA0AbN4MjB4NbNni\n+P2oqCgsX74c1as/gjt35HfcutXxNhaLBd99NwyLFq3H4cMHcObMEiQkHM7ez0k44zlXwIcPS2ss\nIECS8I4drj+zbJkkpytX3PdGATmzGT1aWm3uZGUBP/zgPvFZXbwo95OTa9ckvp2fX1a//w5MmABM\nn+5+Em3XLmDtWqBECWDmTNf9W7cCbdrI87RKFSmK7BUkPpmAvcxdBZyaKgkYAKpWBb7/3nH/vn1S\nFU+YAERHA5984nrcDz6Q4OnUSZ40ztLSgF69JLDGjnUfgB98ALz+ulTazqdXgARgfDzw3nuS7J39\n9hswZw5QoQIwe7bjVVX169fHvfdG4Pp1hRdflJ7iN984/vzGjYnIyIhAu3Y1EBgYiMaN++Dzz1c6\n/A5MwMZyTsD798v3AOCBB4BNm+T0296aNcAzzwAjRwKrVrm+wKekyGl7SAjwzjuSSJ1NnSpxNW6c\ntOSc7d4NDBsG/O1vwKefuu6/cUMS/OzZwKhRrm0UpWRy9+ZN4MABYMEC12MsWQLExQH/+Ifcxvmq\nwC1bgLZt5etatRwnzJViC6JQcJeA164F6taVr2NjXauEL74AYmIAf3+gd2/Ztk+g585JhTxnDjBt\nGtCxo2sbY/x4oFIlCbL0dODjjx33b94MJCRIco+LA8aMcWwR3LwpwT90KPDuu3K8Y8ccjxEfL6ep\no0cDTZu6VhHLlskSvJAQoHNnObW1r1a++y4FYWHV4O8v26GhVXHsWEr2fiZg4zkn4HPngGbN5OuQ\nECkQ7BPP8eMyORcXB9SrJzHz7beOx5w4ERgwQF7cK1SQ+LGXkCCx8PHHQI8e0gKwT/Lp6cCkSbIS\nY9o04K9/dS0QZsyQ0/8lS2Sc06c77t+6VRLq1KmSoBcscGy1XLwo99+nj8RoVJRjgWDt/7ZpI9uR\nkciOU0Cej35+cqZwV5RSuf0jnWVmKuXnp1RWlmxfvKhU2bJKWSyyffOmUk2bKpWWJtsWi1L16imV\nmGg7Rtu2Sq1ebdt+4w2lhg61bU+frlREhFLnzsn29u1KhYcrdf68bB88qFTFirbtjAylHnhAqVWr\nZDsrS6mHHlJq8WLbMd97T6nnnrNtT52q1JNP2rYPHlQqMLC9atQoSkVFRanIyCjl59dYNWwYpVb9\nceAmTZRq0iRO7dq1SymlVKdOSn3xhe0YPXv+n2rWbEj2dp8+i1V09PDs7X/9S6n4eNvtJXxJTwMG\nKPXxx7btXr2UWrrUtv23vym1aJFte/p0pQYNsm0vWSJ/V6tDh5SqUEHiXCmlTp5UKjRUqdRU2c7K\nUqpZM6WWLZNti0WpwYOVmjPHdoxp05Tq2dO2/e67SsXF2Z5DR44oVbmyUmfPyvbZs3Ifx4/bjtmj\nh1Kffmo7xpNPKjVzpuPv0bevbXv5cqXat7dtHzyoVI0atufp9etKBQfbti9eVOrhh5W9vHIrlFKs\ngL3N3x8oXdr26vvbb7b+LyCvvn5+0o8CgEOHpL/bvLntGP36SdUMSGW6bZuc/lkNHy636dhRlnUN\nHCjVaIUKsj8yEhg82FaJzJsnkwqdO8u2n59UGl98AVy6JOtxN2yQKsRq5EgZ43//K9tz5wKTJ2/E\n/v37sG/fPhw8uA/PPfcLBgzYhy5dumDXLrmPkBDbMTp3Blavtm1nZFQFcCp7OyAgGenplbO3z5+X\ntar24uPjs/8lJCTk9tBTPjhXwElJMkFsVaeO4xnaqlVA16627a5dpdeanCzbr78uZ0ShobJdvbq0\nuD78ULaXL5dJre7dZVvTpNWwerUc58QJYMUKiUerkSOlzTF3rlTc778v3wsPl/3h4VLlWu9j61bg\n8mVpk1i99hqwdKn0npWSM7/Bg23727eXi6Os8yH2/V9AJivLlpUzBEBud8oWuvl2twUz6cDahrjn\nHknA1vaDVadOMpnwpz9JgPbo4fgOYL17A19+Kcl582agSRM5/bP35psSFK1bAy1bAj17Ou4fPRoY\nMQIYMkSecNOmOd5H69ay3nH4cAnQvn2BGjVs+4OCgH//W54EmzfLKdyUKY73YW1ZvPSStB86dpR1\nzuqPGbwnnpBTxsxMeSIlJrZAqVLHcPLkSVSqVAmJiUuRlbUk+3hXrsgT2F58fHw+HnHKr3LlHFcy\nOCfghx+W03hA/h6JiZKsrEqVAh57DFi8WNZy79oFfP65430MGyZJeNIk6bW++qq86FtFR0uvddQo\nib1BgxyfI/7+Mtk3bpy0QzIzJU7tDR8ucff3vwNHjkhLzb49EBsLVK4sq4oqVgTq15c2ipU1wa5d\nK4l7yxZZJmqvdm15fCpVkkLF+iJzV/IokckAkZFKHTggX//zn0qNGeO4f906pV54Qb6OiVFq61bX\nY3z6qVLduyv1zDNKHT3q/n4sFqW2bVPqwgX3+8+dk1M/66mas8xMpdavVyohwXaq5WzZMvkdfv3V\n/f5//lPGGRe3XFWpUlUFBQWp8PBw9dhjjymllGrb9oyKjX1Cbd0qv8vatWtVvXr1VN26dVV8/FQV\nHGw71Xz6aaU+/9x2bLAFobu331Zq1Cj5+tIlpe65x/Fvb7Eo9eijSh0+LDH44ouux0hJkb/VY48p\ntXCh+/vZs0epiRMlvtzJylJqw4bcY+/gQbnN1avu9x85Ii0ra3vDWWKiUr17S3vim29c9y9cqNSI\nETKW8uWVOn3acX/fvra2xoYNSrVr57A7Xy0IJmATxMYqtWOHfD1ggFLz5jnuv3VLguLbb5Xq1k2p\nO3dcj2FNrseOGT9eT2RkyAuItT/nbN48eQH6+9+VmjXLdX/FivKEVkqe+GvW2PYxAevv44+VGjhQ\nvv7pJ6Wio11vM22azAm88IJSK1a4P87x47YY92UHDsjv6c7Fi0p16SK/Y/furvvfeMM2J7F0qSRz\nO+wB+6omTVx7wPaCg+V0ffp0mfl1N7OqadKicP5ZXxMYKKd21v6cs6eflj71vn3SWnFWp45txrtc\nOVkLTcYpX962TMy5/WDVs6esWggKknaZOzVrytWMvq5hQ9sqD2ehobJccuZMWR3hzNqCAAregmAP\n2ATXr9ve+ezYMdceMCD9qx49pD9VlJUta3uTF+t6U3u1a0sCfughWajPBGys0FBJJkDOCbhuXeCz\nz6RQcJ4ULWqGDpUJwsqVXffVrg385z/y9eXLjhPM+cUEbIIqVWQC4+ZN+cNVqeJ6G00DwsK8PzYz\nuEu8VvYV8PnzRf8FyWz33WeLu3PnZHLKneLyQujn5/75CUhsHjokX2dk5HyWl+vxCz40Kqhy5WRR\neFKSnKr58a+Qozp15HG6dUtmu8uUMXtERVtYmFztBtjeo4Tcq1JFLiS6fl2KhIJUwHzqm6BSJaku\n3C1BI0d16sha0HPnZOkQP5DTWCEhssY2LU2u7vL1OQYz+fnJ43PsmMxjVKpUgGPoPyzKS7Vq8spp\nfRMeyln9+nKad+aMnC2QsTQNePxxufjmxx/5mOclNlYuxw4NzblVkRsmYBNUry5VRnKyLDqnnFWo\nIIG9dy/bD94SGipXV3bv7vh+B+QqLExaNVeuSGF1t5iATVCrlvx/4QLQqJG5YykMYmPliqoGDcwe\nSfFQu7a8Ixmr37zFxsqVdiEhuU8m54QJ2ASBgbKs5eRJWRNMuXvwQbnktGlTs0dSPDRuLGccrVub\nPRLf16qVXE7t/FYA+aWpnN5ZW+S6kwruzBl5mz1rNUw5u31b3uP4/vsdV4xomoY84pcKICNDTqub\nNCnA2ysWQ4cPS6vM+mZXf8jXdDETMBVaTMDkw/KVgNmCICIyCRMwEZFJmICJiEzCBExEZBImYCIi\nkzABExGZhAmYiMgkTMBERCZhAiYiMgkTMBGRSZiAiYhMwgRMRGQSJmAiIpMwARMRmYQJmIjIJEzA\nREQmYQImIjIJEzB5xVdffYXGjRvD398fu3fvzvF2NWvWRJMmTdC0aVM88MADXhwhkffxE5/IK6Ki\norB8+XK89NJLud7Oz88PCQkJCAkJ8dLIiMzDBExeUb9+fQDI8zPclFKwWCzeGBKR6diCIJ+iaRoe\nffRRtGjRAvPmzTN7OESGYgVMuunQoQNSU1Ozt5VS0DQNkydPRpcuXfJ1jB07diA8PBznz59Hhw4d\nEBkZiQcffNCoIROZKq+PpSfSlaZpWwGMUkrlPBNnu+0EANeVUu/lsF8BmGj3rQSlVIIuAyXyAlbA\nZAbN7Tc1rRQAP6XUDU3TSgPoCMcE60Ap5fY4RIUFe8DkFZqmddc07TSAWADfapq29o/vV9I07ds/\nbhYGYJumaXsA7ATwjVJqgzkjJjIeWxBERCZhBUxEZBImYCIikzABExGZhAmYiMgkTMBERCZhAiYi\nMgkTMBGRSZiAiYhM8v+e2sGTfVJKWwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ccc9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x117ccc588>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(d.doit(), (x, -2*pi,2*pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Wj0sQ6jCA3RADWB2HQwKD1OEShDoMYDfEAFaHHbB67IDVaOgcsowtwgBWxzQZ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\nmvx/tMdSPTSLNXAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d99128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x117d99780>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=Sum(c,(n,1,100))\n",
    "plot(d.doit(), (x, -2*pi,2*pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}