{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Borwein積分\n", "\n", "黒木玄\n", "\n", "2019-06-13\n", "\n", "* Copyright 2019 Gen Kuroki\n", "* License: MIT https://opensource.org/licenses/MIT\n", "* Repository: https://github.com/genkuroki/Calculus\n", "\n", "このファイルは次の場所できれいに閲覧できる:\n", "\n", "* http://nbviewer.jupyter.org/github/genkuroki/Calculus/blob/master/A03%20Borwein%20integral.ipynb\n", "\n", "* https://genkuroki.github.io/documents/Calculus/A03%20Borwein%20integral.pdf\n", "\n", "このファイルは [Free Wolfram Engine](https://www.wolfram.com/engine/) を [Jupyter](https://jupyter.org/) で[使えるようにする](https://github.com/WolframResearch/WolframLanguageForJupyter)と利用できる. 詳しくは次の解説を参照せよ.\n", "\n", "* [Free Wolfram EngineをJupyterで使う方法](https://nbviewer.jupyter.org/github/genkuroki/msfd28/blob/master/Free%20Wolfram%20Engine.ipynb)\n", "\n", "$\n", "\\newcommand\\eps{\\varepsilon}\n", "\\newcommand\\ds{\\displaystyle}\n", "\\newcommand\\Z{{\\mathbb Z}}\n", "\\newcommand\\R{{\\mathbb R}}\n", "\\newcommand\\C{{\\mathbb C}}\n", "\\newcommand\\T{{\\mathbb T}}\n", "\\newcommand\\QED{\\text{□}}\n", "\\newcommand\\root{\\sqrt}\n", "\\newcommand\\bra{\\langle}\n", "\\newcommand\\ket{\\rangle}\n", "\\newcommand\\d{\\partial}\n", "\\newcommand\\sech{\\operatorname{sech}}\n", "\\newcommand\\cosec{\\operatorname{cosec}}\n", "\\newcommand\\sign{\\operatorname{sign}}\n", "\\newcommand\\sinc{\\operatorname{sinc}}\n", "\\newcommand\\real{\\operatorname{Re}}\n", "\\newcommand\\imag{\\operatorname{Im}}\n", "\\newcommand\\Li{\\operatorname{Li}}\n", "\\newcommand\\PROD{\\mathop{\\coprod\\kern-1.35em\\prod}}\n", "\\newcommand\\Si{\\operatorname{Si}}\n", "\\newcommand\\Ci{\\operatorname{Ci}}\n", "\\newcommand\\si{\\operatorname{si}}\n", "\\newcommand\\Cin{\\operatorname{Cin}}\n", "\\newcommand\\Fourier{\\operatorname{\\mathscr{F}}}\n", "$" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "
$$\left(\frac{1}{2}+\frac{1}{3}>1\right)=\text{False}$$" ] }, "execution_count": 28, "metadata": { "text/html": [] }, "output_type": "execute_result" } ], "source": [ "1/2+1/3 > 1 // TeXEq" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "