{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.integrate as integrate\n",
    "import scipy.special as special"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def I( a, g ):\n",
    "    def numerical( x ): \n",
    "        return np.exp( -a*x**2 -g*x**4 )\n",
    "    def partial_sum( nc ): \n",
    "        return np.sqrt(np.pi/a) * np.sum( (-g)**nc/(2*a)**(2*nc)*special.factorial2(4*nc-1)/special.factorial(nc) )\n",
    "    return numerical, partial_sum    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for a,g,ns in [ (1/2, 0.005, np.arange(2, 32, 1)), (1/2, 0.01, np.arange(2, 14, 1)), (1/2, 0.5, np.arange(2, 12, 1))]:\n",
    "    fig, ax = plt.subplots(1,1)\n",
    "    ax.set_title(f'a={a}, g = {g}')\n",
    "    ex, ps = I(a,g)\n",
    "    val, err = integrate.quad(ex, -np.inf, np.inf)\n",
    "    ax.axhline( 1, ls =  '--', label = 'exakt', c = 'red' )\n",
    "    ax.plot( ns, [ ps(np.arange(n))/val for n in ns], 'o', label = 'Näherung' )\n",
    "    ax.set_xlabel(r'$c$')\n",
    "    ax.set_ylabel(r'$I / I_c$')\n",
    "    ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}