Bonjour Colaboratory

Readme.md

Python

meijerg([[0,-2], [1]], [[1/2], [-1/2, -1]], x)

Mathematica (WolframAlpha)

MeijerG[{{0,-2}, {1}}, {{1/2}, {-1/2, -1}}, x]

Voir dans WolframAlpha

meijer_plot.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Bonjour Colaboratory",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/ktzanev/bd204baaf61f71de2a34304864b9dd88/meijer_plot.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "colab_type": "text",
        "id": "TbPKMXi0xZnO"
      },
      "cell_type": "markdown",
      "source": [
        "## Meijer function plot"
      ]
    },
    {
      "metadata": {
        "id": "8DSQIr1osa0w",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Importation de la bibliothèque `mpmath`"
      ]
    },
    {
      "metadata": {
        "id": "5mG7ozI9mUiq",
        "colab_type": "code",
        "outputId": "3010b4c7-5a0d-4202-f2e0-3b204fc0e6e6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "from mpmath import *\n",
        "print('Meijer example for x=2:',float(meijerg([[0,-2], [1]], [[1/2], [-1/2, -1]], 2)))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Meijer example for x=2: 0.21106469777659798\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "qVjN69SksqAY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Définition de la fonction de Meijer avec des paramètres spécifiques "
      ]
    },
    {
      "metadata": {
        "id": "ZsLoTw_TnEJ2",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "mj = lambda x : float(meijerg([[0,-2], [1]], [[1/2], [-1/2, -1]], x))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ucNT1xA-ncwa",
        "colab_type": "code",
        "outputId": "ed136fe8-1f30-427a-e6d8-d77ad09dd307",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "mj(2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.21106469777659798"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "metadata": {
        "colab_type": "text",
        "id": "yv2XIwi5hQ_g"
      },
      "cell_type": "markdown",
      "source": [
        "### Visualisation"
      ]
    },
    {
      "metadata": {
        "colab_type": "text",
        "id": "Y3dN2qDbxZnf"
      },
      "cell_type": "markdown",
      "source": [
        "### importation des bibliothèques pour la visualisation"
      ]
    },
    {
      "metadata": {
        "colab_type": "code",
        "id": "FoYlg8NHxZng",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "WJQ2iCxXtkGR",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Trace la fonction entre 1 et 100 avec un pas de 1"
      ]
    },
    {
      "metadata": {
        "id": "M8sn0nyMn9m5",
        "colab_type": "code",
        "outputId": "a0e7541e-0ca3-41f7-b5f7-485f49032a0e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "cell_type": "code",
      "source": [
        "x = np.arange(1.,100.,1)\n",
        "y = [mj(n) for n in x]\n",
        "_ = plt.plot(x, y, '-')\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFKCAYAAAAnj5dkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nM4QzAAA2QzgDAGAzhDMAADbz/wFmXN2VnrgVugAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f61565a6e10>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "T8Q7WkZmtt3x",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Trace la fonction entre 1 et 2 avec un pas de .02"
      ]
    },
    {
      "metadata": {
        "colab_type": "code",
        "id": "FlQq0SUepQbd",
        "outputId": "2a405030-5f45-4c7f-9dd3-c7369ffd41c7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "cell_type": "code",
      "source": [
        "x = np.arange(1.2,3.,.02)\n",
        "y = [mj(n) for n in x]\n",
        "_ = plt.plot(x, y, '-')\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAFKCAYAAAAnj5dkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAw/OZvGEBJzzAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f61557757f0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "5FpBG5UauJsE",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}