{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 03 π と e とEuler定数 γ\n", "\n", "黒木玄\n", "\n", "2018-04-18～2019-04-03, 2023-06-22\n", "\n", "* Copyright 2018,2023 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/03%20pi%2C%20e%2C%20and%20Euler's%20γ.ipynb\n", "\n", "* https://genkuroki.github.io/documents/Calculus/03%20pi%2C%20e%2C%20and%20Euler's%20%CE%B3.pdf\n", "\n", "このファイルは Julia Box で利用できる.\n", "\n", "自分のパソコンにJulia言語をインストールしたい場合には\n", "\n", "* [WindowsへのJulia言語のインストール](http://nbviewer.jupyter.org/gist/genkuroki/81de23edcae631a995e19a2ecf946a4f)\n", "\n", "* [Julia v1.1.0 の Windows 8.1 へのインストール](https://nbviewer.jupyter.org/github/genkuroki/msfd28/blob/master/install.ipynb)\n", "\n", "を参照せよ. 前者は古く, 後者の方が新しい.\n", "\n", "論理的に完璧な説明をするつもりはない. 細部のいい加減な部分は自分で訂正・修正せよ.\n", "\n", "$\n", "\\newcommand\\eps{\\varepsilon}\n", "\\newcommand\\ds{\\displaystyle}\n", "\\newcommand\\R{{\\mathbb R}}\n", "\\newcommand\\C{{\\mathbb C}}\n", "\\newcommand\\QED{\\text{□}}\n", "\\newcommand\\root{\\sqrt}\n", "$" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

目次

\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "using Base.MathConstants\n", "using Base64\n", "using Printf\n", "using Statistics\n", "const e = ℯ\n", "endof(a) = lastindex(a)\n", "linspace(start, stop, length) = range(start, stop, length=length)\n", "\n", "using Plots\n", "#gr(); ENV[\"PLOTS_TEST\"] = \"true\"\n", "#clibrary(:colorcet)\n", "#clibrary(:misc)\n", "default(fmt=:png)\n", "\n", "function pngplot(P...; kwargs...)\n", " sleep(0.1)\n", " pngfile = tempname() * \".png\"\n", " savefig(plot(P...; kwargs...), pngfile)\n", " showimg(\"image/png\", pngfile)\n", "end\n", "pngplot(; kwargs...) = pngplot(plot!(; kwargs...))\n", "\n", "showimg(mime, fn) = open(fn) do f\n", " base64 = base64encode(f)\n", " display(\"text/html\", \"\"\"\"\"\")\n", "end\n", "\n", "using SymPy\n", "#sympy.init_printing(order=\"lex\") # default\n", "#sympy.init_printing(order=\"rev-lex\")\n", "\n", "using SpecialFunctions\n", "using QuadGK" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Override the Base.show definition of SymPy.jl:\n", "# https://github.com/JuliaPy/SymPy.jl/blob/29c5bfd1d10ac53014fa7fef468bc8deccadc2fc/src/types.jl#L87-L105\n", "\n", "@eval SymPy function Base.show(io::IO, ::MIME\"text/latex\", x::SymbolicObject)\n", " print(io, as_markdown(\"\\\\displaystyle \" * sympy.latex(x, mode=\"plain\", fold_short_frac=false)))\n", "end\n", "@eval SymPy function Base.show(io::IO, ::MIME\"text/latex\", x::AbstractArray{Sym})\n", " function toeqnarray(x::Vector{Sym})\n", " a = join([\"\\\\displaystyle \" * sympy.latex(x[i]) for i in 1:length(x)], \"\\\\\\\\\")\n", " \"\"\"\\\\left[ \\\\begin{array}{r}$a\\\\end{array} \\\\right]\"\"\"\n", " end\n", " function toeqnarray(x::AbstractArray{Sym,2})\n", " sz = size(x)\n", " a = join([join(\"\\\\displaystyle \" .* map(sympy.latex, x[i,:]), \"&\") for i in 1:sz[1]], \"\\\\\\\\\")\n", " \"\\\\left[ \\\\begin{array}{\" * repeat(\"r\",sz[2]) * \"}\" * a * \"\\\\end{array}\\\\right]\"\n", " end\n", " print(io, as_markdown(toeqnarray(x)))\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 準備: 曲線の長さ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**高校数学IIIの復習:** 曲線の長さは速さの時間積分で定義される. すなわち, 曲線 $(x(t),y(t))$, $a 0\\,\\}\n", "$$\n", "\n", "と定義される. これは\n", "\n", "$$\n", "x(t) = \\sqrt{1-t^2}, \\quad y(t) = t\n", "$$\n", "\n", "によって\n", "\n", "$$\n", "C = \\{\\,(x(t),y(t))\\mid -1\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xx(t) = sqrt(1-t^2)\n", "yy(t) = t\n", "t = -1:0.01:1\n", "plot(size=(500, 400), aspect_ratio=1, xlim=(-1.1,1.1), ylim=(-1.1,1.1))\n", "plot!(xx.(t), yy.(t), label=\"C\", legend=:topleft)\n", "hline!([0], color=\"gray\", ls=:dot, label=\"\")\n", "vline!([0], color=\"gray\", ls=:dot, label=\"\")" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{1}{t^{2} - 1}$\n" ], "text/plain": [ " -1 \n", "------\n", " 2 \n", "t - 1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", real=true)\n", "x = sqrt(1-t^2)\n", "y = t\n", "simplify(diff(x,t)^2+diff(y,t)^2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\pi$\n" ], "text/plain": [ "pi" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(1/sqrt(1-t^2), (t,-1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 正弦函数の微積分\n", "\n", "前節の計算より, $-1\\leqq y\\leqq 1$ に対して, \n", "\n", "$$\n", "F(y) = \\int_0^y\\frac{dt}{\\sqrt{1-t^2}}\n", "$$\n", "\n", "は $C$ 上の点 $(1,0)$ から $(\\sqrt{1-y^2}, y)$ までの弧の長さの $\\pm1$ 倍になる. 符号は $y>0$ なら $+$ になり, $y<0$ なら $-$ になる. すなわち, $\\theta(y)$ は弧度法の意味での角度である. 単位円上の $y$ 座標を角度 $\\theta$ の函数とみなしたものを $y = \\sin\\theta$ と定義するのであった. これは, $y = \\sin\\theta$ は $\\theta=F(y)$ の逆函数であることを意味する. $F(y)$ は $\\arcsin y$ と書かれることが多い.\n", "\n", "$\\ds \\frac{d\\theta}{dy} = F'(y)=\\frac{1}{\\sqrt{1-y^2}}$ なので, その逆函数の導函数は\n", "\n", "$$\n", "\\frac{d\\sin\\theta}{d\\theta} = \\frac{dy}{d\\theta} = \\sqrt{1-y^2} = \\sqrt{1-\\sin^2\\theta}.\n", "$$\n", "\n", "これで $\\sin\\theta$ の導函数の計算の仕方もわかった.\n", "\n", "以上の筋道に従えば, 高校数学IIIまでの範囲内で, 三角函数の微分積分学が適切に展開可能なことがわかる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 円周率の定義2\n", "\n", "傾き $t$ の直線 $y=tx$ と単位半円周 $C$ の交点を $(X,Y)=(X(t), Y(t))$ と書くと,\n", "\n", "$$\n", "X=X(t) = \\frac{1}{\\sqrt{1+t^2}}, \\quad Y=Y(t)=\\frac{t}{\\sqrt{1+t^2}}.\n", "$$\n", "\n", "このとき, \n", "\n", "$$\n", "\\sqrt{X'(t)^2+Y'(t)^2} = \\frac{1}{1+t^2}\n", "$$\n", "\n", "となる(自分で工夫して楽な計算の仕方を見付けるように努力してみよ). ゆえに円周率は\n", "\n", "$$\n", "\\pi = \\int_{-\\infty}^\\infty \\frac{dt}{1+t^2}\n", "$$\n", "\n", "と表わされる. これを円周率の定義だと思ってもよい." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** 積分 $\\ds \\int_{-\\infty}^\\infty \\frac{dt}{1+t^2}$ で $\\ds t = \\frac{y}{\\sqrt{1-y^2}}$ と置換すると,\n", "\n", "$$\n", "\\int_{-\\infty}^\\infty \\frac{dt}{1+t^2} = \\int_{-1}^1 \\frac{dy}{\\sqrt{1-y^2}}\n", "$$\n", "\n", "が得られることを確認せよ. $\\QED$\n", "\n", "**注意:** $x=1/\\sqrt{1+t^2}$, $y=t/\\sqrt{1+t^2}$ のとき, $x^2+y^2=1$ より $x=\\sqrt{1-y^2}$ となるので, $t=y/x=y/\\sqrt{1-y^2}$. $\\QED$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $\\ds y=\\frac{t}{\\sqrt{1+t^2}}$ とおくと, $\\ds \\int\\frac{dy}{\\sqrt{1-y^2}} = \\int \\frac{dt}{1+t^2}$ となることも確認せよ. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**注意:** $m>0$ であるとする. 曲線 $x^m+y^m=1$ と直線 $y=tx$ の $x>0$ における交点は $\\ds (x,y)=\\left(\\frac{1}{(1+t^m)^{1/m}},\\frac{t}{(1+t^m)^{1/m}}\\right)$ と表わされる. さらに, $x^m(1+t^m)=1$ より $mx^{m-1}(1+t^m)\\,dx + m x^m t^{m-1}\\,dt = 0$ と $y = tx$ より,\n", "\n", "$$\n", "\\frac{dx}{(1-x^m)^{1/m}} =\n", "\\frac{dx}{y} =\n", "\\frac{dx}{tx} = -\n", "\\frac{x^m t^{m-1}\\,dt}{t x^m(1+t^m)} = -\n", "\\frac{t^{m-2}\\,dt}{1+t^m}.\n", "$$\n", "\n", "上の円の場合は本質的に $m=2$ の特別な場合である. $\\QED$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{t^{2} + 1}$\n" ], "text/plain": [ " 1 \n", "------\n", " 2 \n", "t + 1" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", real=true)\n", "X = 1/sqrt(1+t^2)\n", "Y = t*X\n", "simplify(sqrt(diff(X,t)^2+diff(Y,t)^2))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{\\sqrt{1 - y^{2}}}$\n" ], "text/plain": [ " 1 \n", "-----------\n", " ________\n", " / 2 \n", "\\/ 1 - y " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = symbols(\"y\", real=true)\n", "t = y/sqrt(1-y^2)\n", "simplify(diff(t,y)/(1+t^2))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{t^{2} + 1}$\n" ], "text/plain": [ " 1 \n", "------\n", " 2 \n", "t + 1" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", positive=true)\n", "y = t/√(1+t^2)\n", "simplify(diff(y,t)/√(1-y^2))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{t^{m - 2}}{t^{m} + 1}$\n" ], "text/plain": [ " m - 2 \n", "-t \n", "--------\n", " m \n", " t + 1 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", positive=true)\n", "m = symbols(\"m\", positive=true)\n", "x = 1/(1+t^m)^(1/Sym(m))\n", "y = t*x\n", "simplify(diff(x,t)/y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "以下の問題は https://twitter.com/cc226158/status/1043059177889783810 より.\n", "\n", "**問題:** $\\ds \\int_1^2 \\frac{dx}{(9-x^3)^{1/3}}$ を求めよ.\n", "\n", "**略解:** $x^3 + y^3 = 9$ と $y=tx$ の $x>0$ における交点の $x$ 座標は $\\ds x =\\left(\\frac{9}{1+t^3}\\right)^{1/3}$ になる. これを逆に解くと $\\ds t=\\frac{(9-x^3)^{1/3}}{x\\;\\;\\;}$ なので $x=1$ のとき $t=2$ となり, $x=2$ のとき $t=1/2$ になる. 上の注意と同様の計算によって\n", "\n", "$$\n", "\\frac{dx}{(9-x^3)^{1/3}} =\n", "\\frac{dx}{y} =\n", "-\\frac{t\\,dt}{1+t^3}.\n", "$$\n", "\n", "ゆえに, 置換積分によって \n", "\n", "$$\n", "\\int_1^2 \\frac{dx}{(9-x^3)^{1/3}} = \\int_{1/2}^2 \\frac{t\\,dt}{1+t^3} =\n", "\\frac{\\pi}{3\\sqrt{3}} \\approx 0.6046\n", "$$\n", "\n", "となることが若干の計算によって確かめられる. $\\QED$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{\\sqrt[3]{3} \\left({{}_{2}F_{1}\\left(\\begin{matrix} \\frac{1}{3}, \\frac{1}{3} \\\\ \\frac{4}{3} \\end{matrix}\\middle| {\\frac{1}{9}} \\right)} - 2 {{}_{2}F_{1}\\left(\\begin{matrix} \\frac{1}{3}, \\frac{1}{3} \\\\ \\frac{4}{3} \\end{matrix}\\middle| {\\frac{8}{9}} \\right)}\\right)}{3}$\n" ], "text/plain": [ " / _ _ \\ \n", " 3 ___ | |_ /1/3, 1/3 | \\ |_ /1/3, 1/3 | \\| \n", "-\\/ 3 *| | | | 1/9| - 2* | | | 8/9|| \n", " \\2 1 \\ 4/3 | / 2 1 \\ 4/3 | // \n", "---------------------------------------------------------\n", " 3 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = symbols(\"x\", positive=true)\n", "simplify(integrate(1/(9-x^3)^(1/Sym(3)), (x, 1, 2)))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{t}{t^{3} + 1}$\n" ], "text/plain": [ " -t \n", "------\n", " 3 \n", "t + 1" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", positive=true)\n", "x = (9/(1+t^3))^(1/Sym(3))\n", "diff(x, t)/(t*x)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{\\log{\\left(t + 1 \\right)}}{3} + \\frac{\\log{\\left(t^{2} - t + 1 \\right)}}{6} + \\frac{\\sqrt{3} \\operatorname{atan}{\\left(\\frac{\\sqrt{3} \\left(2 t - 1\\right)}{3} \\right)}}{3}$\n" ], "text/plain": [ " / ___ \\\n", " ___ |\\/ 3 *(2*t - 1)|\n", " / 2 \\ \\/ 3 *atan|---------------|\n", " log(t + 1) log\\t - t + 1/ \\ 3 /\n", "- ---------- + --------------- + ---------------------------\n", " 3 6 3 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", positive=true)\n", "simplify(integrate(t/(1+t^3), t))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\sqrt{3} \\pi}{9}$\n" ], "text/plain": [ " ___ \n", "\\/ 3 *pi\n", "--------\n", " 9 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = symbols(\"t\", positive=true)\n", "simplify(integrate(t/(1+t^3), (t, 1/Sym(2), 2)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 正接函数の微積分\n", "\n", "前節の計算より, \n", "\n", "$$\n", "\\theta = G(a) = \\int_0^a \\frac{dt}{1+t^2}\n", "$$\n", "\n", "は単位半円周上の点 $(1,0)$ から傾き $a$ の直線 $y=ax$ と単位半円周 $C$ の交点までの弧の長さの $\\pm1$ 倍になり, 符号 $a$ の符号に等しくなる. すなわち, 弧度法の意味での角度に等しい.\n", "\n", "正接函数の定義は傾きを角度の函数とみたものであった. これは $a=\\tan\\theta$ が $\\theta=G(a)$ の逆函数になっていることを意味している. $G(a)$ は $\\arctan a$ と書かれることが多い.\n", "\n", "$\\ds\\frac{d\\theta}{da} = G'(a) = \\frac{1}{1+a^2}$ なので, $\\ds\\frac{d\\tan\\theta}{d\\theta} = \\frac{da}{d\\theta} = 1+a^2 = 1+\\tan^2\\theta$.\n", "\n", "以下の公式もよく使われる:\n", "\n", "$$\n", "\\int_0^1 \\frac{dt}{1+t^2} = \\frac{\\pi}{4}, \\qquad\n", "\\int_0^\\infty \\frac{dt}{1+t^2} = \\frac{\\pi}{2}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\pi}{4}$\n" ], "text/plain": [ "pi\n", "--\n", "4 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\frac{\\pi}{2}$\n" ], "text/plain": [ "pi\n", "--\n", "2 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = symbols(\"t\", real=true)\n", "integrate(1/(1+t^2), (t,0,1)) |> display\n", "integrate(1/(1+t^2), (t,0,oo)) |> display" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Machinの公式による円周率の計算\n", "\n", "**arctanのMaclaurin展開:** $|x|<1$ のとき\n", "$$\n", "\\arctan x = \\int_0^x \\frac{dt}{1+t^2} =\n", "\\int_0^x \\sum_{k=0}^\\infty(-1)^k t^{2k}\\,dt =\n", "\\sum_{k=0}^\\infty(-1)^k\\int_0^x t^{2k}\\,dt =\n", "\\sum_{k=0}^\\infty(-1)^k\\frac{x^{2k+1}}{2k+1}.\n", "$$\n", "\n", "詳しくはノート「06 Taylorの定理」を参照せよ. $\\QED$\n", "\n", "**Machinの公式:**\n", "$$\n", "4\\arctan\\frac{1}{5} - \\arctan\\frac{1}{239} = \\frac{\\pi}{4}.\n", "$$\n", "\n", "**証明:** $\\tan$ の加法定理\n", "\n", "$$\n", "\\tan(\\alpha+\\beta) = \\frac{\\sin\\alpha\\,\\cos\\beta+\\cos\\alpha\\,\\sin\\beta}{\\cos\\alpha\\,\\cos\\beta-\\sin\\alpha\\,\\sin\\beta} = \n", "\\frac{\\tan\\alpha+\\tan\\beta}{1-\\tan\\alpha\\,\\tan\\beta}\n", "$$\n", "\n", "より,\n", "\n", "$$\n", "\\tan(\\alpha-\\beta) = \\frac{\\tan\\alpha-\\tan\\beta}{1+\\tan\\alpha\\,\\tan\\beta}, \\quad\n", "\\tan(2\\alpha) = \\frac{2\\tan\\alpha}{1-\\tan^2\\alpha}.\n", "$$\n", "\n", "$a=\\tan\\alpha$, $b=\\tan\\beta$ とおくと, これらは次のように書き直される:\n", "\n", "$$\n", "\\arctan a-\\arctan b =\\arctan\\frac{a-b}{1+ab}, \\quad\n", "2\\arctan a = \\arctan\\frac{2a}{1-a^2}.\n", "$$\n", "\n", "特に, $a=m/n$, $b=(m-n)/(m+n)$ のとき\n", "\n", "$$\n", "\\frac{a-b}{1+ab} = \\frac{m(m+n)-n(m-n)}{n(m+n)+m(m-n)} =\n", "\\frac{m^2+n^2}{m^2+n^2} = 1, \\quad\n", "\\frac{2a}{1-a^2} = \\frac{2mn}{n^2-m^2}\n", "$$\n", "\n", "なので\n", "\n", "$$\n", "\\arctan\\frac{m}{n}-\\arctan\\frac{m-n}{m+n} =\\arctan 1 = \\frac{\\pi}{4}, \\quad\n", "2\\arctan\\frac{m}{n} = \\arctan\\frac{2mn}{n^2-m^2}\n", "$$\n", "\n", "ゆえに, \n", "\n", "$$\n", "\\begin{aligned}\n", "&\n", "4\\arctan\\frac{1}{5} =\n", "2\\arctan\\frac{5}{12} =\n", "\\arctan\\frac{120}{119}, \n", "\\\\ &\n", "4\\arctan\\frac{1}{5} - \\arctan\\frac{1}{239} =\n", "\\arctan\\frac{120}{119} - \\arctan\\frac{1}{239} = \\arctan 1 = \\frac{\\pi}{4}.\n", "\\qquad\\QED\n", "\\end{aligned}\n", "$$\n", "\n", "**問題:** 円周率 $\\pi$ を小数点以下第3桁まで求めよ.\n", "\n", "**解答例:** Machinの公式より,\n", "\n", "$$\n", "\\pi = 16\\arctan\\frac{1}{5} - 4\\arctan\\frac{1}{239}.\n", "$$\n", "\n", "$\\arctan x$ は $|x|<1$ で次のようにTaylor展開される:\n", "\n", "$$\n", "\\arctan x = \\int_0^s\\frac{dt}{1+t^2} = \n", "\\sum_{k=0}^\\infty(-1)^k\\frac{x^{2k+1}}{2k+1} =\n", "x - \\frac{x^3}{3} + \\frac{x^5}{5} - \\frac{x^7}{7} + \\cdots\n", "$$\n", "\n", "$0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# https://twitter.com/genkuroki/status/1024160463729225733\n", "showimg(\"image/jpg\", \"machin.jpg\")" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(a, b) = (1 / 5, 1 / 239) = (0.2, 0.0041841004184100415)\n", "(n, m) = (3, 1) = (3, 1)\n", "\n", "16 * R(a, n) = -2.925714285714287e-5\n", "4 * R(b, m) = -9.766636714833518e-8\n", "16 * R(a, n) - 4 * R(b, n) = -2.9257142857130044e-5\n", "\n", "16a = 3.2\n", "16 * (a - a ^ 3 / 3) = 3.1573333333333333\n", "16 * ((a - a ^ 3 / 3) + a ^ 5 / 5) = 3.1583573333333335\n", "4b = 0.016736401673640166\n", "16 * ((a - a ^ 3 / 3) + a ^ 5 / 5) - 4b = 3.1416209316596935\n", "\n", "π - (16 * ((a - a ^ 3 / 3) + a ^ 5 / 5) - 4b) = -2.8278069900355973e-5\n", "float(π) = 3.141592653589793\n" ] }, { "data": { "text/plain": [ "3.141592653589793" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R(x,n) = (-1)^n*x^(2n+1)/(2n+1)\n", "\n", "@show a, b = 1/5, 1/239\n", "@show n, m = 3, 1\n", "println()\n", "@show 16R(a,n)\n", "@show 4R(b,m)\n", "@show 16R(a,n)-4R(b,n)\n", "println()\n", "@show 16a\n", "@show 16(a-a^3/3)\n", "@show 16(a-a^3/3+a^5/5)\n", "@show 4b\n", "@show 16(a-a^3/3+a^5/5)-4b\n", "println()\n", "@show π - (16(a-a^3/3+a^5/5)-4b)\n", "@show float(π)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(a, b) = (1 / 5, 1 / 239) = (0.2, 0.0041841004184100415)\n", "(n, m) = (8, 2) = (8, 2)\n", "\n", "16 * R(a, n) = 1.2336188235294129e-12\n", "4 * R(b, m) = 1.025889257698589e-12\n", "16 * R(a, n) - 4 * R(b, m) = 2.077295658308238e-13\n", "\n", "16 * f(a, n) - 4 * f(b, m) = 3.1415926535896284\n", "\n", "π - (16 * f(a, n) - 4 * f(b, m)) = 1.6475709685437323e-13\n", "float(π) = 3.141592653589793\n" ] } ], "source": [ "# 小数点以下第12桁まで正確に計算\n", "\n", "R(x,n) = (-1)^n*x^(2n+1)/(2n+1)\n", "f(x,n) = sum(k->(-1)^k*x^(2k+1)/(2k+1), 0:n-1)\n", "\n", "@show a, b = 1/5, 1/239\n", "@show n, m = 8, 2\n", "println()\n", "@show 16R(a, n)\n", "@show 4R(b, m)\n", "@show 16R(a, n) - 4R(b, m)\n", "println()\n", "@show 16f(a, n) - 4f(b, m)\n", "println()\n", "@show π - (16f(a, n) - 4f(b, m))\n", "@show float(π);" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.141592653589793238462643383279502884197169399375105820974944592307816406286198" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BigFloat(π)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Napier数" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 対数函数と指数函数\n", "\n", "このノートでは $x>0$ の(自然)対数函数 $y = \\log x$ を\n", "\n", "$$\n", "y = \\log x = \\int_1^x \\frac{dt}{t}\n", "$$\n", "\n", "で定義し, これの逆函数で指数函数 $x = \\exp y$ を定義しておく. \n", "\n", "このとき, $\\log 1 = 0$, $\\exp 0 = 1$ となる.\n", "\n", "さらに, $\\ds\\frac{dy}{dx}=\\frac{d\\log x}{dx} = \\frac{1}{x}$ が成立し, その逆函数については $\\ds\\frac{dx}{dy} = \\frac{d\\exp y}{dy} = x = \\exp y$.\n", "\n", "これらの条件によって $\\log x$ と $\\exp y$ は一意的に定まることを示せるが, ここではその証明には触れない." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** 上の対数函数の定義だけを用いて $\\log(x_1x_2)=\\log x_1 + \\log x_2$ ($x_1,x_2>0$) となることを示せ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**証明:** \n", "\n", "$$\n", "\\log(x_1 x_2) = \\int_1^{x_1x_2}\\frac{dt}{t} =\n", "\\int_1^{x_1} \\frac{dt}{t} + \\int_{x_1}^{x_1x_2}\\frac{dt}{t}.\n", "$$\n", "\n", "2つ目の項の積分変数を $t=x_1 s$ で置換すると, \n", "\n", "$$\n", "\\int_{x_1}^{x_1x_2}\\frac{dt}{t} = \\int_1^{x_2} \\frac{x_1\\,ds}{x_1 s} = \\int_1^{x_2} \\frac{ds}{s}.\n", "$$\n", "\n", "$s$ を改めて $t$ とおけば欲しい結果が得られる. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** 上の問題の結果を用いて $\\exp(y_1+y_2) = \\exp(y_1)\\exp(y_2)$ となることを示せ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**証明:** $x_i = \\exp y_i$ とおくと, $y_i=\\log x_i$ であり, 上の問題の結果より, $y_1+y_2=\\log(x_1 x_2)$ なので\n", "\n", "$$\n", "\\exp(y_1+y_2) = \\exp\\log(x_1 x_2) = x_1 x_2 = \\exp(y_1)\\exp(y_2).\n", "\\qquad\\QED\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$a>0$ に対して, $a^y$ を\n", "\n", "$$\n", "a^y = \\exp(y\\log a)\n", "$$\n", "\n", "によって定義する. このとき, 整数 $n$ について\n", "\n", "$$\n", "a^1 = \\exp(\\log a)) = a, \\qquad\n", "a^n = \\exp(n\\log a)) = (\\text{$n$ 個の $\\exp(\\log a))$ の積}) = (\\text{$n$ 個の $a$ の積}).\n", "$$\n", "\n", "後者で上の問題の結果を使った. これより, 整数の $n$ について, 上の定義に基いた $a^n$ と $n$ 個の $a$ の積が一致することがわかった. 上のように定義しても混乱は生じない." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Napier数の定義\n", "\n", "このノートでは Napier数 $e$ を\n", "\n", "$$\n", "e = \\exp(1)\n", "$$\n", "\n", "によって定義する. すなわち $e$ は\n", "\n", "$$\n", "\\int_1^e \\frac{dt}{t} = 1\n", "$$\n", "\n", "という条件で定義されているものとする." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**定理:**\n", "$$\n", "\\lim_{n\\to\\infty}\\left(1+\\frac{y}{n}\\right)^n = \\exp(y).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**証明:**\n", "\n", "$$\n", "\\left(1+\\frac{y}{n}\\right)^n = \\exp\\left[n\\log\\left(1+\\frac{y}{n}\\right)\\right]\n", "$$\n", "\n", "である. $d(\\log x)/dx = 1/x$ の $x=1$ の場合より, $h\\to 0$ のとき, \n", "\n", "$$\n", "\\frac{\\log(1+h)}{h} = \\frac{\\log(1+h)-\\log(1)}{h} \\to 1.\n", "$$\n", "\n", "これを $h=y/n$, $n\\to\\infty$ の場合に適用すると, \n", "\n", "$$\n", "\\frac{\\log(1+y/n)}{1/n} = y \\frac{\\log(1+y/n)}{y/n} \\to y.\n", "$$\n", "\n", "ゆえに, $\\exp$ の連続性を用いると, $n\\to\\infty$ のとき,\n", "\n", "$$\n", "\\left(1+\\frac{y}{n}\\right)^n = \\exp\\left[n\\log\\left(1+\\frac{y}{n}\\right)\\right]\\to \\exp(y).\n", "\\qquad\\QED\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "上の定理の $y=1$ の特別な場合として次が得られる.\n", "\n", "**系:**\n", "$$\n", "\\lim_{n\\to\\infty}\\left(1+\\frac{1}{n}\\right)^n = e.\n", "\\qquad\\QED\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "以上によって, 対数函数と指数函数とNapier数 $e$ の理論が微分積分学を用いてすべて再構成された." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.718281828459045235360287471352662497757247093699959574966967627724076630353555" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BigFloat(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Euler定数\n", "\n", "以上によって, 数学における基本的な定数 $\\pi$ と $e$ の定義が明瞭になった.\n", "\n", "しかし, それだけで終わってしまうと, 高校の数学で習うことを単に再構成したに過ぎなくなってしまう. \n", "\n", "そこでこのノートではその次に知っておくべきだと思われるEuler定数 $\\gamma$ について説明しよう.\n", "\n", "Euler定数とその歴史については次の文献が詳しい:\n", "\n", "* https://arxiv.org/abs/1303.1856" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler定数の定義\n", "\n", "数列 $a_n, b_n$ を次のように定める:\n", "\n", "$$\n", "\\begin{aligned}\n", "&\n", "a_n = \\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} - \\log(n+1)\n", "\\\\ &\n", "b_n = \\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} - \\log n.\n", "\\end{aligned}\n", "$$\n", "\n", "$y=1/x$ は狭義単調減少函数なので\n", "\n", "$$\n", "\\begin{aligned}\n", "&\n", "\\log(n+1) - \\log n = \\int_n^{n+1}\\frac{dx}{x} < \n", "\\frac{1}{n} < \n", "\\int_{n-1}^n \\frac{dx}{x} = \\log n - \\log(n-1),\n", "\\\\ &\n", "\\log(n+1)=\\int_1^{n+1} \\frac{dx}{x} < \n", "\\frac{1}{1}+\\frac{1}{2}+\\cdots+\\frac{1}{n} \n", "\\end{aligned}\n", "$$\n", "\n", "となる(図を描いて確認せよ). 後者より, \n", "\n", "$$\n", "0 < a_n < b_n\n", "$$\n", "\n", "が成立していることがわかり, 前者より, \n", "\n", "$$\n", "\\begin{aligned}\n", "&\n", "a_n - a_{n-1} = \\frac{1}{n} + \\log n - \\log(n+1) > 0, \n", "\\\\ &\n", "b_n - b_{n-1} = \\frac{1}{n} + \\log(n-1) - \\log n < 0.\n", "\\end{aligned}\n", "$$\n", "\n", "となり, $a_n$ は単調増加し, $b_n$ は単調減少することがわかる. (図を描けば, $a_n$ が単調増加し, $b_n$ が単調減少することは見た目的に明らかになる.)\n", "\n", "したがって, $a_n$ も $b_n$ も収束することがわかる.\n", "\n", "\n", "さらに, $0<\\log(n+1)-\\log n<1/n$ より $a_n$ と $b_n$ の収束先が同じであることもわかる.\n", "\n", "それらの収束先を $\\gamma$ と書き, **Euler定数**と呼ぶ.\n", "\n", "$$\n", "\\gamma = \n", "\\lim_{n\\to\\infty}\\left(\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} - \\log(n+1)\\right) = \n", "\\lim_{n\\to\\infty}\\left(\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} - \\log n\\right).\n", "$$\n", "\n", "この定義は次のように書き換えられる:\n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} = \\log n + \\gamma + o(1).\n", "$$\n", "\n", "ここで $o(1)$ は $n\\to\\infty$ で $0$ に収束する項を表す." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**考え方:** 解析学では\n", "\n", " (調べたい量) = (相対的にわかりやすい量) + (誤差)\n", "\n", "の形式で考える. Euler定数の定義は, 調べたいもの\n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n}\n", "$$\n", "\n", "を相対的にわかりやすい量\n", "\n", "$$\n", "\\log n + \\gamma\n", "$$\n", "\n", "プラス誤差の形式で認識することであるとみなせる. $n$ が大きなとき, 第1項の $\\log n$ と比較して第2項の定数項 $\\gamma$ は小さいとみなせ, 第2項 $\\gamma$ と比較して誤差項 $o(1)$ は小さいとみなせる. $1/1+1/2+\\cdots+1/n$ を $\\log n$ で大雑把に近似するより, $\\log n + \\gamma$ で近似する方がより精密な近似になる. \n", "\n", "このように新たに項を付け加えることによって近似の精度を逐次的に高めて行くことは, 解析学における典型的なパターンであり, あらゆる場所で出会うことになる. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**注意:** digamma函数 $\\psi(s)$ ($s>0$) を\n", "\n", "$$\n", "\\psi(s) =\n", "-\\lim_{n\\to\\infty}\\left[\\frac{1}{s}+\\frac{1}{s+1} + \\cdots + \\frac{1}{s+n} - \\log n\\right]\n", "$$\n", "\n", "と定めることができる. これはガンマ函数が\n", "\n", "$$\n", "\\Gamma(s)=\\lim_{n\\to\\infty}\\frac{n^s n!}{s(s+1)\\cdots(s+n)}\n", "$$\n", "\n", "と書けることを使えば $\\psi(s)=d\\log\\Gamma(s)/ds$ とも表わされる. ガンマ函数に関するこの公式については\n", "\n", "* ガンマ分布の中心極限定理とStirlingの公式\n", "\n", "の第8.2節を参照せよ. Euler定数の定義より $\\psi(1)=-\\gamma$ であることがわかり, digamma函数の定義より $\\psi(s+1)=1/s+\\psi(s)$ であることがわかるので, 帰納的に非負の整数 $n$ について\n", "\n", "$$\n", "\\psi(n+1) = \\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} - \\gamma\n", "$$\n", "\n", "であることがわかる. この公式はdigamma函数 $\\psi(s+1)$ は調和級数からEuler定数を引いたものの連続的な補間になっていることを意味している. したがって, $\\psi(s+1)$ の $s\\to\\infty$ での漸近挙動がよくわかれば, 調和級数の漸近挙動もよくわかることになる. \n", "\n", "ガンマ函数については次のStirlingの近似公式がよく知られている: $s\\to\\infty$ において\n", "\n", "$$\n", "\\log\\Gamma(s+1) = s\\log s - s + \\frac{1}{2}\\log s + \\log\\sqrt{2\\pi} + \\frac{1}{12s} + O\\left(\\frac{1}{s^2}\\right).\n", "$$\n", "\n", "これを $s$ で微分することによって, \n", "\n", "$$\n", "\\psi(s+1) = \\log s + \\frac{1}{2s} - \\frac{1}{12s^2} + O\\left(\\frac{1}{s^3}\\right) \\qquad (s\\to\\infty).\n", "$$\n", "\n", "以上をまとめると次が得られる:\n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} =\n", "\\log n + \\gamma + \\frac{1}{2n} - \\frac{1}{12n^2} + O\\left(\\frac{1}{n^3}\\right) \\qquad (s\\to\\infty).\n", "$$\n", "\n", "このように調和級数 $\\ds\\frac{1}{1}+\\frac{1}{2}+\\cdots+\\frac{1}{n}$ の $n\\to\\infty$ における漸近挙動の詳細はガンマ函数に関するStirlingの公式の対数微分によって得られる. $\\QED$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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plot!(p, x, f.(x), color=:blue, label=\"log($n)\", fill=(0, 1.0, :pink))\n", " x = n:0.05:n+1\n", " plot!(p, x, f.(x), color=:blue, label=\"log($(n+1))\", fill=(0, 0.5, :pink))\n", " plot!(p, [1,1], [0,1], color=:red, label=\"1/1+1/2+...+1/$n\")\n", " for k in 1:N\n", " x = k:0.05:k+1\n", " g(x) = 1/k\n", " c = ifelse(k > n, :pink, :red)\n", " plot!(p, x, g.(x), color=c, label=\"\")\n", " plot!(p, [k+1,k+1], [0,1/k], color=c, label=\"\")\n", " end\n", " x = 0.1:0.05:N+2\n", " plot!(p, x, f.(x), color=:blue, label=\"y=1/x\")\n", " plot!(title=\"n = $n\", titlefontsize=10)\n", " p\n", "end\n", "\n", "N = 6\n", "p1 = plot_eulergamma(N, N-1)\n", "p2 = plot_eulergamma(N, N)\n", "plot(p1, p2, size=(700, 300))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16-element Vector{Tuple{Int64, Float64, Float64}}:\n", " (1, 0.3068528194400547, 1.0)\n", " (2, 0.4013877113318902, 0.8068528194400547)\n", " (3, 0.4470389722134427, 0.7347210446652235)\n", " (4, 0.47389542089923276, 0.6970389722134425)\n", " (5, 0.49157386410527826, 0.6738954208992329)\n", " (6, 0.5040898509446865, 0.6582405307719448)\n", " (7, 0.5134156011773068, 0.6469469938018293)\n", " (8, 0.520632565520923, 0.6384156011773068)\n", " (9, 0.5263831609742078, 0.6317436766320341)\n", " (10, 0.5310729811698831, 0.6263831609742079)\n", " (100, 0.5722570007983601, 0.5822073316515279)\n", " (1000, 0.5767160812351229, 0.5777155815682065)\n", " (10000, 0.5771656690678633, 0.5772656640681966)\n", " (100000, 0.5772106649431983, 0.5772206648931988)\n", " (1000000, 0.5772151649019452, 0.5772161649014453)\n", " (10000000, 0.5772156149015366, 0.5772157149015307)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aa(n) = sum(k->1/k, 1:n) - log(n+1)\n", "bb(n) = sum(k->1/k, 1:n) - log(n)\n", "[(n, aa(n), bb(n)) for n in [1:9; @.(10^(1:7))]]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "γ = 0.5772156649015..." ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eulergamma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 条件収束交代級数への応用\n", "\n", "次の2つの数列を考える:\n", "\n", "$$\n", "A_n = \\frac{1}{1} + \\frac{1}{3} + \\cdots + \\frac{1}{2n-1}, \\quad\n", "B_n = \\frac{1}{2} + \\frac{1}{4} + \\cdots + \\frac{1}{2n}.\n", "$$\n", "\n", "このとき\n", "\n", "$$\n", "A_n + B_n = \\sum_{k=1}^{2n}\\frac{1}{k} = \\log(2n) + \\gamma + o(1), \\quad\n", "2B_n = \\sum_{k=1}^n \\frac{1}{k} = \\log n + \\gamma + o(1).\n", "$$\n", "\n", "ここで $o(1)$ は $n\\to\\infty$ で $0$ に収束する項を意味する. ゆえに, \n", "\n", "$$\n", "A_n = \\log 2 + \\frac{1}{2}\\log n + \\frac{\\gamma}{2} + o(1), \\quad\n", "B_n = \\frac{1}{2}\\log n + \\frac{\\gamma}{2} + o(1).\n", "$$\n", "\n", "これより, $n\\to\\infty$ で\n", "\n", "$$\n", "A_n-B_n \\to \\log 2.\n", "$$\n", "\n", "すなわち,\n", "\n", "$$\n", "\\frac{1}{1} - \\frac{1}{2} + \\frac{1}{3} - \\frac{1}{4} + \\cdots = \\log 2.\n", "$$\n", "\n", "より一般に正の整数 $p,q$ について\n", "\n", "$$\n", "A_{pn} = \\log 2 + \\frac{1}{2}(\\log p+\\log n) + \\frac{\\gamma}{2} + o(1), \\quad\n", "B_{qn} = \\frac{1}{2}(\\log q + \\log n) + \\frac{\\gamma}{2} + o(1)\n", "$$\n", "\n", "なので, $n\\to\\infty$ のとき\n", "\n", "$$\n", "A_{pn}-B_{qn} \\to \\log 2 + \\frac{1}{2}\\log\\frac{p}{q}. \n", "$$\n", "\n", "**例:** $p=2$, $q=1$ のとき\n", "\n", "$$\n", "\\frac{1}{1}+\\frac{1}{3}-\\frac{1}{2} +\n", "\\frac{1}{5}+\\frac{1}{7}-\\frac{1}{4} +\n", "\\cdots = \\frac{3}{2}\\log 2.\n", "$$\n", "\n", "$p=1$, $q=2$ のとき\n", "\n", "$$\n", "\\frac{1}{1}-\\frac{1}{2}-\\frac{1}{4} +\n", "\\frac{1}{3}-\\frac{1}{6}-\\frac{1}{8} +\n", "\\cdots = \\frac{1}{2}\\log 2.\n", "\\qquad \\QED\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**考え方:** 以上のような計算が可能になったのは, \n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n}\n", "$$\n", "\n", "が大雑把に $\\log n$ で近似できることだけではなく, より精密に\n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{n} = \\log n + \\gamma + o(1)\n", "$$\n", "\n", "の形で漸近挙動がわかっているからである." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "S = A(2n) - B(n) = 1.0397207458399187\n", "T = (3 / 2) * log(2) = 1.0397207708399179\n", "S - T = -2.499999918192941e-8\n" ] } ], "source": [ "A(n) = sum(k->1/(2k-1), 1:n)\n", "B(n) = sum(k->1/(2k), 1:n)\n", "\n", "n = 10^7\n", "@show S = A(2n) - B(n)\n", "@show T = 3/2*log(2)\n", "@show S - T;" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2.500000007010783e-8" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(k->1/(4k-3)+1/(4k-1)-1/(2k), 1:10^7) - T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler定数がガンマ函数の無限積表示に出て来ること" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$s>0$ のとき, ガンマ函数 $\\Gamma(s)$ が\n", "\n", "$$\n", "\\Gamma(s) = \\int_0^\\infty e^{-x} x^{s-1}\\,dx\n", "$$\n", "\n", "によって定義され, digamma函数 $\\psi(s)$ が\n", "\n", "$$\n", "\\psi(s) = \\frac{d}{ds}\\log\\Gamma(s) = \\frac{\\Gamma'(s)}{\\Gamma(s)} =\n", "\\frac{1}{\\Gamma(s)}\\int_0^\\infty e^{-x} x^{s-1}\\log x\\,dx\n", "$$\n", "\n", "によって定義される. \n", "\n", "ガンマ函数について次が成立してることが知られている(Weierstrassの公式):\n", "\n", "$$\n", "\\frac{1}{\\Gamma(s)} = \n", "e^{\\gamma s} s \\prod_{n=1}^\\infty\n", "\\left[\\left(1+\\frac{s}{n}\\right)e^{-s/n}\\right].\n", "$$\n", "\n", "この公式の証明については\n", "\n", "* ガンマ分布の中心極限定理とStirlingの公式\n", "\n", "の第8.2節を参照せよ.\n", "\n", "Weierstrassの公式より\n", "\n", "$$\n", "-\\psi(s) = \\gamma + \\frac{1}{s} - \\sum_{n=1}^\\infty\\left[\\frac{1}{n}-\\frac{1}{n+s}\\right].\n", "$$\n", "\n", "特に\n", "\n", "$$\n", "-\\psi(1) = -\\int_0^\\infty e^{-x}\\log x\\,dx = \\gamma = 0.5772156649015\\cdots.\n", "$$\n", "\n", "Euler定数 $\\gamma$ は次の積分表示を持つことも示せる:\n", "\n", "$$\n", "\\gamma = \\int_0^\\infty\\left(\\frac{e^{-t}}{1-e^{-t}}-\\frac{e^{-t}}{t}\\right)\\,dt.\n", "$$\n", "\n", "この公式の証明については上の文献の第8.7節を参照." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5772156649015328606065120900824024310421593359399235988057672348848677267776685" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "-digamma(big(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler定数が高次元単体上の一様分布に関連して自然に出て来ること\n", "\n", "$r>0$ に対して, $n-1$ 次元単体 $\\Delta^{n-1}(r)$ が\n", "\n", "$$\n", "\\Delta^{n-1}(r) = \\{\\,(x_1,\\ldots,x_n)\\in\\R_{\\geqq 0}^n \\mid x_1+\\cdots+x_n = r\\,\\}\n", "$$\n", "\n", "と定義される. ここで $\\R_{\\geqq 0}$ は非負の実数全体の集合を表す. 例えば, $n=3$ のとき\n", "\n", "$$\n", "\\Delta^2(r) = \\{\\, (x,y,z)\\in\\R^3\\mid x,y,z\\geqq 0,\\; x+y+z=r\\,\\}.\n", "$$\n", "\n", "は点 $(r,0,0)$, $(0,r,0)$, $(0,0,r)$ を頂点とする正三角形になる.\n", "\n", "$\\Delta^{n-1}(n)$ 上の一様分布(例えば $n=3$ の場合には正三角形上に一様に分布する確率分布)を考える. \n", "\n", "そのとき, $\\Delta^{n-1}(n)$ の点の第 $i$ 座標 $x_i$ の分布(例えば $x_1$ の分布)は $n\\to\\infty$ のとき確率密度函数が $\\exp(-x)$ の指数分布に近付くことを証明できる. \n", "\n", "ゆえに, $n\\to\\infty$ で $\\log x_i$ の期待値は $\\int_0^\\infty e^{-x}\\log x\\,dx = \\psi(1) = -\\gamma = -0.5772\\cdots$ に近付く.\n", "\n", "このような形でも自然にEuler定数 $\\gamma$ が自然に出て来る.\n", "\n", "このような現象は「統計力学」ではよく知られている. 詳しくは次のノートを参照せよ:\n", "\n", "* Kullback-Leibler情報量とSanovの定理" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** 次のセルの `rand_Uniform_on_Simplex` 函数がどうして $\\Delta^{n-1}(1)$ 上の一様分布に従う擬似乱数を発生させる函数になっているかを説明せよ. \n", "\n", "**ヒント:** $(x_1,\\ldots,x_n)$ を $(x_1, x_1+x_2, \\ldots, x_1+\\cdots+x_{n-1})$ に対応させる写像を考えよ. その写像を通して, 単体 $\\Delta^{n-1}(1)$ 上の一様分布と $n-1$ 次元立方体 $[0,1]^{n-1}$ 上の一様分布をどのように関係付けられるかについて考えよ. $n-1$ 次元立方体はその成分の並び方の順序で分類することによって $(n-1)!$ 個の部分集合に分割される(境界の重なりは無視してよい). $\\QED$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "plot_Uniform_on_Simplex (generic function with 1 method)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# r = 1 の場合の n-1 次元単体上の一様分布に従う擬似乱数を発生させる函数\n", "function rand_Uniform_on_Simplex(n)\n", " Z = sort(rand(n-1))\n", " return vcat(Z, 1.0) - vcat(0.0, Z)\n", "end\n", "\n", "function rand_Uniform_on_Simplex(n, N)\n", " X = zeros(n, N)\n", " for j in 1:N\n", " X[:,j] = rand_Uniform_on_Simplex(n)\n", " end\n", " return X\n", "end\n", "\n", "# x_1 の分布と log x_i 達の平均の分布をプロットする函数\n", "function plot_Uniform_on_Simplex(n; N=10^4)\n", " X = n*rand_Uniform_on_Simplex(n, N)\n", " ElogX = vec(mean(log.(X), dims=1))\n", "\n", " p1 = plot(xlabel=\"x\", xlim=(0, 7.5), title=\"n = $n\")\n", " histogram!(p1, X[1,:], normed=true, alpha=0.5, label=\"x_1\")\n", " plot!(p1, x->exp(-x), 0, 7.5, lw=2, label=\"exp(-x)\")\n", "\n", " p2 = plot(xlabel=\"x\", legend=:topleft, legendfontsize=7)\n", " xlims!(-eulergamma-0.3, -eulergamma+0.3)\n", " histogram!(p2, ElogX, normed=true, alpha=0.5, linealpha=0.1, label=\"mean of log x_i\")\n", " vline!([-eulergamma], lw=2, label=\"x = $(round(Float64(-eulergamma),digits=5))\")\n", "\n", " plot(p1, p2, size=(700, 300), layout=grid(1,2,widths=[0.35, 0.65]))\n", "end" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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T8+mnn+bm5np4eEyZMmXNmjUJCQm7d+/+4Ycf/P39PTw8Tp48ef78eWtJBADXrl0bOnRo7969L1y40KtXr7lz565cudJgMCxcuHDgwIFDhw6tFamqqqpPnz6tW7euqKigKOqXX34hSfL1119PT09v1apVXl6e0Wjcv3+/tb9Wq+3fv//Bgwc9PDx69OixfPnyO4uGF154Ye7cuZ06dbK21ExoD0iSVKlU9yoaFAq9jJcBACuVUyQlPOAi46+QuTJmY6JC/JcjFA0Ot4ZsLaL/GB+RbfPbV9FAc3y13MvNpHblHPsDA9VSXFw8atSo5cuXx8bGGgyGkSNHTp8+vVevXnf2HD58OADs27evsSM2pKKiIp7nhe/fjqKiomLjxo0KhWLixIlXr17dvHkzwzBBQUEWi+XChQvJycnHjh0jCGL37t3z5s1bs2bNZ599BgAmkykxMXHx4sWbNm0CAJZlhVVbxo0bd+DAAeGXK5g9e/b7778/adIkmqajoqImTZr02WefLV68ePny5XfNs2zZsh49eggre/br12/Pnj2tWrU6dOhQWloaSZKLFy/es2dPzf5hYWFffPHF2LFjg4KCxo8f/8QTTzTcz8quEARB3HtAC6FHZF9FAwBUufi5mdTuDBYNTiUwMHDMmDHPPvvs2bNnp02b5u7ufteKwUFdu3bt6NGjKSkpOTk5P/30U6tWrXr06PHnn3+mpaW1adOmqqpq7ty5o0aNuteou32KjY0VviAGBQUJl5KRSCQ+Pj6VlZV///13bm5uv379AMBkMgmnh6xbt27p0qU+Pj48z1tHiYSVYQEgJCTEehkaQVpamrAeuVQq7dSpU1paWsuWdU2qSEtLGzJkiLDdrVu3y5cvkyTZvn174YhPx44daxUNADBy5MhVq1Zdu3bt559/ftQfB0IIAOyyaPBvpr7qzjjV9SERALzyyitHjhzp1auXRqM5d+6c2HFsqby8/Pz5835+fn5+fufPnxcO3jdv3nzPnj2HDh1yc3N75ZVXaq6E5hCs0y8Igqg1FcPLyysxMXHDhg3WFp7np0+fnp2d7eLi8tdff1kXpbBOgCAIgv/3xRG8vLyElekBoLS0tNbcgjt5eXmVlpZa+z/22GP+/v4FBQVCi3WjppMnTxYUFEil0kOHDvXpY5vpogg1cfZXNCj9AMCNxZEGJ/Tyyy/37dt30aJFjn6MsJZu3bp169atVuNjjz32ww8/iJKnoQ0aNGjmzJlr167t3r17YWGhVqt9+umnlUrl8ePHQ0JC7rp67J1efPHFWbNmLVmyJCUlpaysrEuXLnX3Hzt27IsvvtipU6eKiordu3fPmDHD39/faDR++eWXrVu3/uGHH2pN4KqsrHz55Zc3b97s6uo6YMCAY8eO1ZwmiRB6OPZXNLgIRYNB7CDIxjQazeTJk2fNmjVv3ryhQ4e2aNFC7ETOQF9eVFmQbZNdcSxr3Q4ICBg9erSw3aNHD3d3d2F78uTJLi4urq6uJ06cWLx48d69e4OCgsaNGwcAO3bs+P777728vGbPnn358mUAaN26tfWMiZ49e9Y6OvPSSy8pFIqvvvoqICDg8OHDwkf+W2+9VSuVj4/P2LFjASAhIeHHH39csWKFXC7fu3evcMTkwIEDa9asycvLmzp16q5du2o+MDk5ef78+cLxke+///7cuXODBw+utfPnnntO2A9CqJ7srmjQqgIAwIPGosHZvPbaa4MGDfr000+9vb1HjRp18uRJuVx+Z7fs7Ozs7Oz8/HyJRHLgwIGWLVuGh4c3eljH8ERCp01bNpYc2mibvXXtat0ODg6ePHmysN2/f39r+7vvvits+Pn5ff755zUf3rFjR+HECgDo3r07ALRv3946p+GuF6sbPXq0tTQRfPrpp7X6+Pn5vf7668J27969rYs+CVJTU4cMGWIymaZOnTplypSadyUlJd11uybra0QI1ZPdFQ0alR8AuLM4p8GpnDhxguf5hQsXAsCbb76ZkZHx66+/jho16q49rQfL58+fP3HiRCwa7mXqq69MffUVsVOISa1WL1++nKKoKVOmjBkzpu7OAwYMqHku93/+8597FRMIoXuxu6LBIPegJQo5Y+KMelIp8sok6K5UKlVO2vlFfWqf9X4nhra8+OJ4AOjevbvw7RMACIL4/vvv7/WQF1988cUXX7RVVOTchg8fXvM0zrr9+eefDRoGoabA7ooGANAqfX10+ay6mGwm/rq26E5xcXHq8vJ6LsBlvVT0nbZv316rJSkpqY7+yHEdPHjwm2++oSjq//7v/2rNeUxJSVmwYIGw3bFjxw8++AAARo8ezd6eYxEYGLh48eJDhw79+OOP1ke98MILgwcPXr9+/fbt28vLy+Pj42fOnOnt7V1WVjZ//vyzZ88qFIrx48cL8yGaII6hC9QmE8MBgIdSIvrSkMhp2GPRUOXi76PLZ9RFUiwa7NWjr1PE87wwXa6mBrouERJXXl7eSy+9tG/fPqPROHTo0IsXL9a83ENBQYHJZJo1axbUeF+9//77wimay5YtYxgGANq2bSvUExzHJSUlffTRRwBQXl4+a9asZs2affbZZ2+88cbPP/+sVqtjYmLefPPNqqqqYcOGhYSEONOKIPXHMvTmLF7mRvEcOyzEGI9FA7IRuywaVH4AwJTjtS6dGUEQd856u6/du3cPHjz4rqvq1nLmzJnw8HCcG//Qpk2b1qdPn6FDh169evWDDz7YsmXLQy8G/N///nfEiBGtWrUCgD59+uzYsaPWqhXe3t6hoaG+vr7W36ywnDbP80ePHt28eTMA+Pr6CheSOHDgQEREhDDF8p133hH6T5gwQdhnbGys9QLfTz755OXLl5tm0QAApEQqVag4hgZw4Es/IHtjx0WDukjsIMi+bN++/ddff7UuC1i3wsLCxYsXO/dSgBWbFjLFN221N0Ku8Hp2miSguXBz+vTpvXv3jo6OHjdu3Pz582tVDAkJCQbDv05xmjRp0ttvv33XPd+4caN169bCdsuWLXNycmp1OH78+JAhQ3Jzc+fPny+cwCk4evSoUqmseW0IAFi9evXEiRNr7WHVqlW13hglJSX79+8XBicQQrZin0VDAAAwZYViB0H25csvv6x5VLtuw4cPf//9969fvx4dHd2gqUTD83Tedbo411b7I+RKtlpr/YvQrFmzr7/+ulOnTu+//37fvn1rdRZOh6nZYl38UZCSknLlyhUAGDZsGMMw1nslEonFYqnZc9CgQcOGDQOA69evd+3aNSkpSRhRAIDVq1dPmjSpZmeNRrN3796lS5fWbFyyZMnVq1e/++47a4terx8xYsSMGTOioqIe5GfgGPgaxM6Cmhy7LBpchMMTWDQ4lfPnz7/77ruZmZlBQUELFizo1avXmTNnZsyYsXPnTjc3t7S0tKlTp27bts3V1TUxMXHKlCkLFiygaXratGnCEHRqaqow363WblmWHTdu3PDhw5977jme56dMmRIfHz958mSCIIYOHbphw4Zaywk4D4II+PCnBn2Gmzdvurq6Vlff5fznQYMG1boM6dixY1999VXrTb1eL6z6zDBMcHBwYeGtf84FBQW1PsitKzlGR0eHhoZmZ2cLRUNVVdWePXsWLVpUs/PGjRsHDBhQc0rEypUrN23atG/fPutYiMFgGDx48LPPPutwS3fXh8ViOXi9XMeQPM/fLNOCHx6AQ43KHosGrcqPI0jQlPG0hZDKxI6DajNnXtSf/A3q8S2HIEhJYKh7vzGlZWWDBg3auHFj3759k5OThdlwXbp0iYiIePnll9euXTt27Ng333zT399fp9OdP3/+xIkTaWlphYWFiYmJrVu3TkpKOnr0aEJCwp1PIUzI79u3b7t27fbu3fvPP/8sWbJEuCs+Pt5ZF3JuBBcvXvz+++8vXrw4fPjw3bt31xr8X79+fa3TZ2otDV5zIaahQ4eOGTPmo48+slgsv/3226FDhwDg6NGjXl5ebdu2zcnJCQ0NJUny7NmzeXl51pGhzZs39+vXr9b1rFevXi2s9iFYt27dsmXL9u/fb12z0mw2jxw5sl+/fvc6VuLoeJ7PMMgqKC/guGpzhYvYeVBTY49FA0dQekrhzhgYdbE0MFTsOKi26jN7jf8cq29vknJNHLp169YOHTpERkZmZ2f7+fnFxcUdOXLkueee++677xISErp06RIXF1dzIPrjjz+WyWTh4eGTJ0/esmVLUlJSXl6e9doBNE0LB9SlUqlKpWrbtu2sWbOGDh1aUVFx+vRp60KTwcHBubk2G71vUiwWywcffLB+/fqAgICNGzdOmDChZ8+eNU+ZeaAZph06dJg0aVLnzp0B4P/+7/8iIiIAYM+ePTExMW3btl23bt2qVaukUqmLi8v69es9PT2FRx0+fLjWio0ZGRkKhaLmxMZVq1ZpNBphz15eXufOnUtOTr527dq1a9dWrlwJAFOnTrWuYokQenT2WDQAQBXl4s4YWHUhFg12yHP4q8rHut6/HwAAUN7+pNK1oKAgMzPzww8/FBq9vLyE9RiUSuXw4cNnz569bNmymo8KDg4WNkJCQk6fPg0AJElav9pu27Zt+vTpANC7d29h+cjhw4e/9957gwcPrnlJi5qH0tEDkclk1qWQIiMjjx2rd414D++99957771Xs8U6YDBr1izhfMtatmzZUqslKirq1KlTNVvuDJaYmJiVlfWIaRFC92KnRYNW4gLmMpwLaZ9IF3dl+x4P9JDw8PDQ0NCtW7fWaj979uyPP/74+eefT5o06dy5c9brG2VlZQnn1GVkZISGhgJARETE3r17hXvHjBlTc81gYVrD66+/vnPnzh07djzzzDNCe0FBgfClFiGEkE2QYge4uyqJCgCYcjzr0kmMGTMmIyPjiy++yMnJuXbt2k8//XTz5k2NRjN69Ohly5Z98skn8fHxb7zxhrX/jBkzsrKyDhw4sGLFCuH8ut69eycnJ991GcovvviC47j58+dv2bJl6tSpN27cENpPnz6Nq0UhhJAN2WnRoJW4AJ5A4UTc3NySk5NLSkrGjh07efLk69evu7m57d69e8qUKSNGjACApUuXchyXnp4u9H/ttdcmT548b968VatWCWdMxMTEtGjR4s7h6NLS0uvXr//8888URXXu3Hnu3Lk7duwAAIZhdu/ejZexQAghG7LTwxOaWyMNWDQ4j6CgoFrXqar5ie7q6rpu3ToA0Ol0ANC3b9+BAwfW2sPnn3++aNGiWgv8+fv7b9q0yXrTuuzPpk2bhgwZ0qxZM1u+BoQQatrstGjQUS5AkkxFKc8yBGWnIVEj6927t7e3N8/z9VlGukePHsIYBkIIIVux089jliAlXv6MupitKJH4hYgdBzUeFxeXrKws64I/tbRr166e+4mMjLRdKPui0WhqLaqIHp1wWSznw3NcZZW2WC0FAJmE9PZwFzsRcmx2WjQAgMQvhFEXM2UFWDQ0KSRJOvHn/aMLCwuLi4sTO4VzCg8PFzuC7fEce6iQO2agAKCDi3Zkeywa0COx66IBrp5nSvOhde2VgxFqstLS0hrz6XQ6Xa2lHh2Lo+e3CYIkpQoVAABoRY6CHJ89nj3BmE2XLl9OuVkGACVXL4sdByGEEEIA9lk0WEzVN6rYS66tAcBou4v4IYQQQuhR2OnhCUoiheiucGWV0qgROwv6l8LCwvPnz4ud4sFkZGSIHQEhhJyBnRYNAKB3DWAJidxSzVtMhEwhdhwEABAbG7t48eLk5GSxgzywpKQksSMg9PA4jqNpGgDMZjPHcYDXVEEisd+igSPISoWXr7GMKSuUhuB0erswevRoXGMRocZnMBhWX9ITlIQ2mypNHOUtdiDUVNnjnAYrtdwXAJjSfLGDIISQyEpYpZryKuddaJ4XOwtquuy7aFD4AgBdViB2EIQQQgjZd9FQrhBGGvLEDoIQQggh+y4aKhTeAGAqzKmqquJxRA4hhBASlV0XDdfVegAwFt58d96SRl4IDyGEEEK12HXRUM1JdCCVAxinFcgAACAASURBVOvmF+asl5NBCCGEHIVdFw0AUES4AoAvXSl2EIQQQqips/eioRCEogHXhUQIIYREZr+LOwkKCVfgwc+CRQNCCD0SlmWEZSUBQCqVihsGOSj7LxrcAA9PIITQI7tSVKVmlQDgL2OHtvHFugE9hPoenrh48WLXrl19fHx69Ohx9erVWvfyPN/p35YsWQIAOTk5NRv/+9//Pmi+QnABAD+66kEfiBBCqKZqmiilfEopnzILXrsCPaR6jTRwHDdy5MgpU6a88cYbCxcuHDVqVGpqas0OBEEsX75c2DYYDH379m3Xrh0AmEymGzdu/PXXX8JdzZs3f9B85YSKkcjdmGoLbXrQxyKEEELIhupVNBw7dqyqquqdd94hSfKDDz5YtGjR2bNn4+Pja/bp2LGjsLF+/frw8PDu3bvfegKJxHrXQ+ABqtxCfCqzJZqyh94JQgghhB5dvQ5PXL16NS4ujiRJAJBKpa1atbrzCIXV6tWrJ06cSBCEcFOj0Tz22GOdO3eeMWOGwWB4iIgaz1AAIDXFD/FYhBBCCNlKvUYaKioqXF1drTc9PDzUavVde2ZnZ586dernn38Wbvr6+m7ZsqVNmzbFxcVvv/12QUHB6tWr63gii8Xy9dffgLEKci9c+OyzYE7dIiqq3DW4BQCUF+r1+vq+LPtQXV0tdgRbMpvNJEk6zeQplmWtpS1CCKH6qFfR4O3trdPprDerqqp8fX3v2nPlypUDBgwIDg4Wbvr6+g4bNgwAoqKili5d2qdPnxUrVlDUPefgyGSy19/5j1lTenLz0qH/N+vSHz9XVGm0PpEAINeraxYujsIRM9+LVCp1sqLBbDaLnQIhhBxJvQ5PREVFXblyheM4AGAY5urVq1FRUXd2Y1l248aNEydOvOtOFAoFy7LCTh6IxiMUACSa0gd9IEIIIYRsqF5FQ+/evVUq1Q8//EDT9LfffhsUFJSQkAAAu3fv/vLLL63d9u7da7FYBg4caG05efLk5cuXLRZLVlbW+++/P3DgwIf4nqpzC6IJijRUcSanGu1HCCGEHEu9igaSJLdv375mzRofH59t27Zt2bJFOBhcUlKSmZlp7ZacnPzOO+/ULAtu3LgxdOhQd3f3Xr16RURErFix4iEicgSplnkCzzMleQ/xcIQQQgjZRH1XhOzQocP58+drNU6ePHny5MnWm7Nnz67VYdy4cePGjXuUfIIyqVegWU0X35SFxT763hBCCCH0EOz9glWCUpkXADDFuWIHQQghhJouBykapF4AQBffFDsIQggh1HQ5StHgDQB04Q2xgyCEEEJNl2MUDZVSd14qZ6vUXLVW7CwIIYRQE+UYRQMPwHr4Ax6hQAghhMTjGEUDADBegQBAF+WInAMhhBBqqhyjaKgsyU9TGwHg+qkjFotF7DgIIYRQU+QYRYO6tPiw0QcAjCX5DnfZKoQQQsg5OEbRAACawNYAEMjqgefFzoIQQgg1RQ5TNFSTSqPSSw4sX3X3q3IjhJCTYRjGfBuP35eQHajvMtL2oMIzPMRYyZXehMhosbMghFCDy1VX7y82kRRl1FVZCDeZSuxAqMlzmJEGAKjwjgQADheTRgg1DRaWryBcNRIvNacUOwtCAI5VNKg9IwCAK8GlGhBCCCEROFLRIIw08Fg0IIQQQmJwpKJB49GMISiuspQzGcTOghBCCDU5jjQRkiOoMtI1iK2iC2/II9uIHQehWywWy6VLl7Kzs9u3bx8VFWVt12q1mzdvrqioGDBgQPv27UVMiBBCNuFIIw0AUEy5AQBdkCV2EIT+p0ePHqNGjXrttdd+//13a6PJZHriiSf27dtnMpn69Onz559/ipgQIYRswpFGGgCgmHIHALogW+wgCP3P4cOHVSrVgAEDajZu3bpVLpdv376dJMmQkJDPP/+8VgeEEHI4DjbSUCSMNBRi0YDsiEp1l9PnDxw4MGDAAJIkAWDQoEGnT5/GFdARQo7OAUcaCIIuyuFZhqAcLDxqUgoLC+Pj44XtgIAAgiAKCwujo++5Lplarf72228DAgKEm8HBwVOnTm2MoHUym80ymUzsFA/P0fPTtIVhGIJiWY4FnmRZlmVZjmFZlgWO41iWZVkAYBmW43kA4DiOYRj2VjshbDC3u916IADLMGazmeO4hs9PsyxLEERDP1HDcfS30APll0gkFEXdp88jR2pUZkJCeAXwFcVMca40JFLsOAjdE0VR1j/KwgLAdf9rpCjK3d3dy8tLuOnl5SWMUoiLJEl7iPHQnCA/IQACiH8B4lYLAJDkrY/lmp3g9jZ5u9vtdgCCaJyfDEmSPM87+q+g6eSvT3nnYEUDAFDBEUxFsSU/E4sGZM+CgoKKioqEbWEjKCiojv6enp4TJ058/PHHGyNcvUmlUqlUKnaKh+fo+SlKQlHUrb/71O1PeurWx4D184AgyVtlAUlY+xNwq///ut1+IEVRjfaTIUnSoX8Fjv4Wsnl+xyugiIBwAKDzM8UOglBdkpKSfvvtN4ZhAGDXrl2JiYl3nfqAUOPjeZ67TewsyME44khDJA1gwaIB2Y2lS5cePXr0woULxcXFp06deuutt7p16zZixIivv/56wIABbdq0Wb9+/c6dO8WOidAtpRVVmy9YJFKplOAHx3hgOYvqz/GKBiIwHAiCLsgCjgNHPtSEnEavXr1iYmKmTJki3GzRogUAyGSyo0eP7tmzp7y8/OzZsy1bthQ1I0L/Y2Qhk/OR8HLSpH0ar7iNHoQDFg1KF4l3AKMupkvzpYGhYsdBCNq0adOmzV2WKFUqlc8991zj50EIoQbikN/Upc1aAgCdlyF2EIQQQqgJcciiQdY8CgAsedfFDoIQQgg1IY5ZNIRGA4AlF4sGhBBCqPE42JyGgptZm7bv8lBKnyQIuiAL14VECCGEGo2DjTQUlmlSIOIkEVNJKHjaUn3zurAqKkIIIYQamoMVDQDg1ayFR2DoxUoLAKz9YdmWX3aJnQghhBBqEhyvaAAAjmOvWFQAEOHjVW2ixY6DEEIINQkOWTQAwHWTFACCdbliB0EIIRtjWZamaZqmWZYROwtC/+KoswgzzRKWkvoaSiQcjjQghJxKyo3yixoCAMpLtIy7p8SBr8yMnI2jjjTQPFHhGU4A716tFjsLQgjZUpWFK+C9CgmfchrrBWRfHLVoAIAy31gA8NKXih0EIYQQahIcuGgo9YsBAM/qMrGDIIQQQk2CIxcNvrEA4IEjDQghhFCjcOCiQesWZJC6yBkToy4WOwtCCCHk/By4aACAAvdwALDkXBE7CEIIIeT8HLxocA0FAEs2Fg0IIYRQg3PsoiHfPQIAzDjSgBBCCDU8xy4ailyb8wRJF+VwJoPYWRBCCCEn59hFA0NKqlx8gOMsOeliZ0EIIYScnKMuI21V6RrgqS+zZF1WxHYUOwtCCDkSY7Xul0uMXCEHgMTmrgE+HmInQvauvkVDdnb24sWLy8rKBg4cOHbs2Ds7zJo1y2w2C9vt27d//vnnhe2///57+fLlZrN5zJgx/fr1s0nomircAiKKL5uzL9t8zwgh5NxYDi4aPVRST8Zs7MTgxbHQ/dXr8IROp+vevbtMJhs6dOjMmTOXLVt2Z59vv/0WALy8vLy8vFxcXITGzMzM3r17x8TE9O7d+/nnn9+/f78NowOAXl2y8cx1HsCQnXb18iXb7hwhhBBCNdVrpGHTpk2RkZFfffUVACiVyv/85z+vvvoqQRC1ur366qvh4eE1W5YuXTpy5Mh33nkHAMrLyxctWvTUU0/ZJjgAANBGfaGqWYU776PNr86+Ao/F2XDnCCGEEKqpXiMNycnJPXv2FLZ79uyZlZVVVnaXKz4sXLhw+vTpO3fu5Hn+zgcmJiYmJyfbIvO/kJS0JKg9ACjKbtp85wghhBCyqtdIQ1FRUVzcrS/x7u7ucrm8qKjI39+/Zp9nnnkmKirKaDS+9957e/bsWbNmDQAUFxf7+PgIHXx9fTUajdFoVCqV93oihqa3bdvOVVdUZWWtW7dOUZ7hFxBgsVg4lmMYxmKx8BxLMzTwLMtxFouFZhiG4/K9Y1rDb5KSG3q9/iF/DA2jurpa7Ai2ZDabSZKUSqViB7ENlmXvHC1DCCFUh3oVDUql0jrJkWVZmqZVKlWtPqtXrxY2nn/++cjIyJkzZ0ZERNR8oNlspihKJqvr8vAUJYmPj6e15WmlV5/o0aMwxcCyvFQqJUmSoiipVEoQpISSSCQUSRBSqVQikVAkWRbUFgBUlYUqhQJIOzqJlOO4O39QjouiKCcrGmiaFjsFQgg5knoVDc2bN8/LyxO2hY3g4OB7dQ4PD3d3dy8qKoqIiGjWrFlubq7QfvPmzeDgYIqi6ngigiTCwkLNGkWum1tkZGT1VY+KKg1BEEAAQRAEcft/VgAEgNHFVy3z9LFomMIsWWhMfV96wyNJkrSnIuYRkbeJHcQ2rAfREEII1VO9PgCeeeaZXbt2aTQaANiwYUNSUpJwfsShQ4cuXboEABqNxmKxCJ1//fVXmqZbtWolPHDz5s0MwwgPfOaZZxroZdxQNQcAc0ZqA+0fIYQQQvUaaUhMTOzTp0+HDh1atmyZlpb2559/Cu3z5s3r1q1bXFzciRMnJkyY0KZNG5PJlJGRsXLlSi8vLwB44YUXfv7558cff9zd3b28vPzw4cMN9DJuKEM6aS6ZM1Ld+jzXQE+BEEIINXH1KhoIgli/fv2VK1fKyso6depkXYZh06ZNcrkcAJ5++unU1NSsrCyFQtGqVSs3Nzehg1KpPHTo0D///GM2mzt37txwh8NvqJoDQZizL/MMTUic5KA7QgghZFceYBnp1q1b12rx8/OzboeEhISEhNz5KJIkO3Zs8AWeq3ipycVboVeXpJ4J7NijoZ8OIYQQaoKcZFJbUeblkxoCAA5u3lBUVCR2HIQQQsgJOUnRwPN8pv/jABBGGjiOEzsOQggh5IScpGgAgAxZMEeQzekKoM1iZ0EIIYSckPMUDQZSXu4TRfEc5F0XOwtCCCHkhJynaACAguDHAYDPSRM7CEIIIeSEnKtoCOoAAMRNLBoQQo6Hvo1lWbGzIHR3D3DKpf0r9Ys1E1J5eSGrKUvLLRKuLODr6xsWFiZ2NIQQqgvLsnuvluUZJQCgLtPwfv54OTVkh5yqaOAIKov0bM2W3Tz255y9l1SxPcwGXWdv+j9TJogdDSGE7qPCQpZSPgBgYMsUYodB6K6c6vAEABwvZwDg+onjF6/dCOs2yL9NAoeXJUIIoTpxLJNfXpVVXJlVXKmu0okdB9kvZysazhmVABDDqwFwtQaEEKoXjqH35JFrbshWZ1JpJUax4yD75WxFQxkrKVcFSGnDYyocYUAIofoiKEoiU1AyudhBkF1ztqIBADK8WgNAgjsjdhCEEELIqThh0ZDp1QoAEtzwnCWEEELIlpywaMj1iLRIVREKzlVfInYWhBBCyHk4YdHAEVReUAcACMtPFjsLQggh5DycsGgAgJvNOgNAaP4ZsYMghBBCzsM5i4bcoE4sTwSVpClog9hZEEIIISfhnEWDReZysZokOSZCfUXsLAghhJCTcM6iAQBOaSkAaFl+SewgCCGEkJNw2qLhRJWEJ4iI8ssUh+deIoQQQjbgtEVDCU2Ue7eUseYAQ7HYWRBCCCFn4LRFAwDkhHUDgObafLGDIIQQQs7AmYuG7LDuABCiL+BZXFIaIYQQelTOXDToXIPKXEOkrMV8/R+xsyCEEEIOz5mLBgBI920HAHn7d54/f16tVosdByGEEHJgTl40/C0P4wHIG5cX7kpOvXhR7DgIIVQbexvP82JnQeg+JGIHaFgVUo8sVtWSMnT0IAH/QSKE7IzJZNqVXqFnSI5jiyqrwc9f7EQI1cXJRxoA4KTFGwAeq0oXOwhCCN1FrlmeR/rlgXc1zthGds/5i4ZTtDdPEDG6LJKxiJ0FIYQQcmBOfngCANSctCggLrj4omvhVYAkseMghJD94jk2Nbe8zEADQLCK7BIVSBCE2KGQHXH+ogEAMiOeDC6+6J6XJnYQ1ITQND127FjrzUGDBo0fP17EPAjVB8/zBWapmg0EAEt1aQLPY9GAamoSRcONsO5dkn9QVeQz6mKJT6DYcVCTwLLstm3bNmzYIJfLASA6OlrsRAgh9KiaRNFAS5XpblHtqtIMfx92f2q02HFQEzJixAiVSiV2CoQQsg3nnwgpuODZBgAMyfvxxEvUmMaPH//888//8MMPDIMz4xFCDq9JjDQAQJZrBK1yh/JCc9Ylecu2YsdBzo+iqJkzZ3bu3LmysnL+/PmnT5/esGFDHf3z8vLGjBmjVCqFmxEREevWrWuUpHXR6/ViR3gk9p/fZDKZTbSFt3CMxWwxUxYLANAWmrRYSIqiGTNvNpMSGU1beJa3WCwW2sKZLaTFAhxHm2mL0J82sxwLACzLmc1mUiq3WCwEkJTFwlgsjIUmLRYAsFgsltsbnNnMAWGhLUDIJBaLxULzjOV2f4vQ38ibdDodST78d0uaplmWpWnaJj8rUdj/W6huD5RfoVBIpdK6+zSVooEH0DaP87l2svrMXiwaUCOQSqWfffaZsJ2QkBATE/Pdd995e3vfq39gYOAHH3wQGxsr3PTz83Nzc2uMoPdjJzEemp3nl0qlckU1I5VxJPAyuUwmAwBGJpXJZCRFSSVymVwuk8ksUhlQEplMBrSMk8tkMhlwHC2XCv1ZqZwiKQCgKFIul8tkMkYmI4CQyWQkx5CyW91kMtmt/jKZVC6XyGSMVAZSqUwm42RSngSZTEYCR97upiQVbm5uj140KBQKm/ysxGLnb6H7sm3+plI0AEBVaFufjNPG1BPciKmkylXsOKgJadasGUEQlZWVdRQNUqm0VatWjz/+eGMGQwihB9JU5jSUZV/5YtMf13l3nrYU7N8udhzk/HJycioqKgCA47gvv/wyNDQ0IiJC7FAIIfRImkrRwDI0Gd0jN/ENAOAvHMbpkKihpaSkhIeHh4eH+/n57dmzZ/v27Y8yzIucjMViqazSVVbpNFU6hz7kj5qaJnR4AgBymydoJC6elSXmjFR5dHux4yBn9uyzzw4dOrS4uNjNzc3Ly0vsOMi+aA2mBf+YKYnMYqQlBKfA03KRg2haX304gvxb2RIA9Cf2iJ0FOT+ZTBYaGooVA7oriVQuU7lK5HKxgyD0AJpW0QAA511aAEkZL59hNWViZ0EIIYQcSZMrGqpJJdvyceBY/fHdYmdBCCGEHEmTKxoAgGnfGwCqT/3Jm41iZ0EIIYQcRlMsGnj/UHlkG86or045IHYWhBBCyGE8wNkTKSkp6enpcXFxHTp0uPNeg8Fw4sSJ0tLS6Ojo+Ph4obG6uvr06dPWPjExMc2bN3/ExI/oRnrqZ9+nx7sQwwH0R3a6PjEI8EQ4hBBCqB7q+3k5e/bskSNHnjx5cvDgwQsXLqx1b3V1dWBg4Ny5c/fv3//ss8+OHj2a53kAyMvLGzRo0Pzbzp07Z+P4D85gtvBxA0sHzVITSqa8yHDhmNiJEEIIIcdQr5EGtVo9b968CxcuREdHX7x4sXv37q+88krN5azlcnlqaqqw4F1ZWVl4ePjZs2cTEhIAwNPTc//+/Q2U/uFQUhmlUJ2kQoYwmbqDW1UdegJBiB0KIYQQsnf1GmnYv39/dHR0dHQ0ALRt2zYoKOjIkSM1O0gkEusSuT4+PnK53Gw2CzdZlj18+PCZM2cMBoMtgz+yrVkaI6WgC7IPrftR7CwIIYSQA6jXSENBQUFISIj1ZkhISH5+/r06L1myJCgoqEuXLsJNV1fXRYsW5efnl5WV7dixw9p+VxzLpaamMrqKcrX63LlzmtISqVTGcRzwwHEcx3HA8xzHcRzBCRs83NrghP9y/O2N2w+51cBzvNCTv9WfK6oyng7r/2T2Lvf04zT9cv1+XA+GpmlnWiCWpmlnWgiZZVkeVxNHCKEHUa+igWXZmp8WEomEYZi79vzzzz/nzJnz119/CVdWjYqKunHjBkEQAPDpp59Onjz50qVLdTwRz/MlpaWsrsJoMBQWFvKGand3qfBJzwNwHCf04fhbNQF/uzgAnr+1AberB/hX9cADD7eKBhDqBgC49tiILvmHAs0Vpmt/S1u2q/cPrb5YlmVZ1ua7FYvwKes0dQPLssLbACF0VxzHWr8qSKVSseMgu1CvoiEoKKis7H/rJ5aUlAQHB9/Z7eDBgxMmTPj111/btbv1AUxRlPXeMWPGzJ4922w2y++9bColofo99ZRZU3qy5MqQIUMu/aGvqNJIJBKCJCiSlEgkQBAURUkoiiQJiURCUaSwQVIkSZESiYQgSYlEIpFICIKQSCQSCUWSpEQiIUmSv7VBUBQldODlLn9H9O9+bbvx4Fa3xxLq+zOrN4ZhHP1C8jURBEGSpNP87WBZ1noQDSF0p8yiqjWslCAITwkzrLVPHX+6UdNRr2+NPXr0uHDhQnl5OQAUFhZeu3atW7duAGAymfR6vdDn5MmTY8aM2bJlS9euXe+6k3/++cff39/e3nYXw3obKZnlRprpSorYWRBCyI4YOCgEryLSp9giEzsLshf1GmkIDw8fNWrU4MGDx44du27dupdeeikwMBAAvv766/379x8+fLiioiIpKSk6Onrz5s2bN28GgPHjxz/xxBMLFizIyMiIjY3Ny8tbvXr1okWLGvbVPDiLRHFeEd69+nrFrhV+LdtJZfhvAyGEELq7+i7utGrVqo0bN6anp7/11ltjxowRGgcMGNC2bVsAkMvltQoCHx8fABgxYsTvv/9eUFAQGBh49OjR9u3t7mrUxir1txdK28Yo3Etyz2xc1mPiW2InQgghhOxUfYsGiUQyYcKEWo0dOnQQVod0cXGZMmXKnY9q0aLFtGnTHi1hw+I4zuLqfzG+f/cz3wdnnOLZ1wnqAVbJRAghhJoOJ5kJ/4iut+xXqvSXG6vw0pcIoYZjNpv1er1er6+ursaTd5AjwqIBAIAjyP0hTwGA7q/NnEEndhyEkHO6Uqyb/7flqwvs0lSjM52PjZoOLBpuyXSP0nqHcgad9o91YmdBCDknHgBkSlLpylNOcuoyamqwaPifnOgeBCXRn/rjRvLR7OzsnJwcXDEQIYQQssKi4X9MKm/XHkOA4wq2Lp+z9dgXyzbodHioAiGEELoFi4Z/cUsaZ5GqwtmKp8J8ebkLjjQghBBCVlg03EKbjHm5uelZN067xwBA/N9r3DhcYxghhBD6H1yT4BZNUc62nJxUi096qtovpkXr6qwB/FWxQyGEEEJ2BEcabuN5uX94aM9npG7evwQ8ZZEo2zAl9KWTYsdCCCGE7AUWDXdRIXU/23ESAJj/WMPqKsWOgxBCCNkFLBru7mpUUpbElzfoKn/+GnA6JEIIIYRFwz0RxMI8ykhITekp+7/+VOw0CCGEkPiwaLinHB3zR+sXASA6P4UuyBY7DkIIISQyLBrqcjOsx+WIPhTPqdd8wZmqxY6DEEIIiQlPubyPE3Ev+uel+JcXlq6Zm/lYfyAIAGjdurW3t7fY0RBCCKFGhSMN98FS0t/c25IqV+baufTftq+8ZPj2r0uZmZli50IIIYQaG4403F8VqfJ+4YOyn2Ymma9Jgp49zoWKnQgh5Egu3CjJ0TIAUKrRcVIlJXaeB6XRandfrpZKJATAU1FeKpVK7ERINDjScD88X1lemsWpCiK7EAC9Ti4KNpeJnQkh5Ehu6tgLdMAFJjBbTzniFW2MFu4fo/cFJjBZ68JxnNhxkJhwpOE+zAZ9ytWcb/5KK87kx0iDEumiMXm/7tl783JmjkImHTawPxbdCCGEmggcabgvHqSqZonPuIQ/tpJrVRDUzp03Pam5nE6E7buQo9VqxY6HEEIINRIsGh4AA8SBnp/k8i5BnG5cxlp1zvUvlqz6cO63S1asFTsaQggh1OCwaHgwtFS1gGlTLPXyqbgx3T0fWvZkO426lF0gdi6EEEKowWHR8MC0vPQ7v6GVHqGRMnp85joPuVTsRAghhFBjwKLhYego1d6+n5cwkiB93sAjn7nwtNiJEEIIoQaHRcNDqlb5flzkW6n09a/IGG9OZdTFYidCCCGEGhYWDQ+vlKXWtX+7zCvShzfmzntt608/njqTLHYohBBCqKHgOg2PpFrmvitxVodNEzu6Gjte/X3N2VOHz14gAEb06xkbGyt2OoQQsiWeY00mRiKRAABFUVIpzuhqcnCk4VFZJIqPb7pmRfSSc/QU19Joik1jAkpKSsTOhRASE8/zOp1Oq9VqtVqTySR2HNugTcbvLxi++Vv/9TntjTKd2HGQCHCkwQYYHg53ey9Lz/YtO941Y7enWxRJPy12KISQmBiG+fmK/qZFBQBMRbUqROxAtsDzfDWpJORerMXM8Eax4yAR4EiDjRDEMd+EL43RZplbK11Gs0OrzNmXxc6EEBITSVEylatM5QpAiJ0FIdvAosGWUhmPXwd9k6cMlhq0ZUummw7+l2cZsUMhhBoVd5sjXpsKobrh4Qkb07kGrYwY8x/2tGfGadPh7ddTjmTH9OL9Qwf0e4og8NsGQk7OaDT+eV1j5oCl6ZIqBrx9xU6EkC3hSIPtVZYWrS0izkQllXNSF315m7936PdtZgx6sXMhhBocz/Pp1YprnP9V2quaxpEG5GywaLA9Q2XZeYPnYd/er+b5HwtMBCCf4IqK5ky6vnNNQX6+2OkQQgihh4RFQ4NQePj4RbZmpfK/QvrvGvhduoEgDVrVsS3q7981Z6SKnQ4hhBB6GFg0NDi1d8SbmcqDXf+jVfp4m6vKln5QtvQDc+YlsXMhhBBCDwYnQjYGHiAjLPGyMqL9kfmJ0gpzRmpZRqq8ZVu3Ps8pYjtCjQmSpaWlDMMAgI+Pj1wuFy8yQgghVBsWDY1Hq9MuvEEc7zW2Y9Hpp5hMyLxozrwoDQx17Tlc1akPIZVVVVXN+GY55+pv+4UPxAAAIABJREFUMRoGPh4xasQwsSMjhBBC/4NFQ6MiFW6B3Yf/vke3K0M3IljayZTjXZxbueW74q1L6RYdKkLaVJqh9ciXS65ftDA5YodFCCGE/gWLBhFwLGMK65z7zMT133/YLyqkP5MZUJkpz0xxzUyZapGVp+8ysD6gFDslQqjeaJo2m80AYDAYWLZJzBVjGJqmaQAgSZKiKLHjoEaCRYOYWCAu+XawdHrz/OzRrzzZJTbvREswtDz3UwIQVe6B+mCJsk0C5eUvdkyE0H2UVhmWXbaQEqm52kSQMoVK7EANjKXNBzK1KeUkAMR58vEtAsROhBoJFg124YaZOvLYuCOhA4zb5zzfMaZ5frKntkizfalm+1KtyrvMo3mld2i/0S+qXN3utYejJ05dzykAAHeVbNSIoY2YHSEEPA+8VEEqVLzZAhwndpzGUMoqtODDc1wzs1rsLKjxYNFgRxhKerxa6dfzo8r0lIHa452UFn1asruhwt1QAUWpZbP2GrybZXNK15j2Bjf/0LDQNq1bWx+bfPFqujRC5elbfWrHc8OH4JLVCDUCmqZZlgUAk9kE4OzDC/dQpdUVlisAQEqRvp5u+MfHuWHRYI+q9PodGer8To9fIPS+odEJLmaPi781B9qt7EY7ADh1hSPIMlKZHtHa7B3SPD7Rp2VrAPAMCvMICqtO3iF2fISaiksFmiPFQBCEqUpLy6RShdiBGh3PcedL2VSWAoAouf6FDi44v8G5YdFgjwwa9TW9UiprlVqS7Bfsz3dK2vVHcr9xb8aa8+n9q7pEBnlqbgaw1ZCZ4gYpxrO/3pQpu1gklYYSoy6O53WcUU+p7nkgAyFkKyYWNIQbKZGaeIPYWURESBUqACCgWuwkqME9QNFgMpmMRqOXl9e9OrAsq9FoPDw8JJJ/7dZgMNA07eHh8fAxmx6Zi5tfZGuZi6u1RS/zuOYftqto86hpS/NP/UZcOTawa2fJ37+Hg9bLYowEgPyjkH+0O0DRR8+Cm5fEv5ncL0TiG0R5B0h8gyTegaQr/goa233/1SBHdCajKL+aB4Diiipe5Xrf/gg5jfoWDQsWLJgzZ45CoQgPD9+5c2dwcHCtDidPnhw9ejTP8zRNr127NikpCQA4jnvzzTc3bdokkUi6deu2efNmlaqJHvazLTMpy+bcQ9o8e+rvXKlfeO/ExMyfPozv0DFcaoZLB8NdKJmuktFVMln/WqyakCsl3gGkpx/h4kF6+PAu7hJPP9LNS+4TIPXw5oCwWCwAQJIkLkZpE3PmzFmwYIFcLo+KitqxY0dAAM4wdwY8z9/U8+lcAACYTXpKiZeyvKWsUns0gydJUkZApzAvmUwmdiJke/UqGi5dujRnzpzz58+3aNFi8uTJH3744fr162t24DhuwoQJs2bNmjRp0p49e1588cW8vDy5XL5z5859+/bl5OS4urr269fv66+//uSTTxrmhTRpepXf3yYVHZSYG/3Yph0nxi7YZrx0SLN3RYfwIKW+PFDGB8jA1aJTmI10UQ4U5dx1JxaC0vJSEyUzARUb11bp5UsoXUmlC6l0JZUuhNKVoaSUQkm5eREyOSGRNuYLdETnzp37+uuvU1NTQ0NDx48f//HHH69cuVLsUAg1oHIjd6jSg5JIVBZN2yALRVEsy/I8FlVOpV5Fw8aNG4cMGdKiRQsAePvttzt16rRixYqaX0ZPnz5dUVExfvx4ABg8eLCHh8e+ffuGDBmyadOml156ydPTEwDeeOONjz76CIuGxkAQFZR7qiwiaNS8czuWV1u4x58cemrdgpadesU1D7i2ZWGvwWNklQX6tJOtYluRxRmujN6d4GQ86wsssCYAYC4c1dX5DByQLCXhJHJXL29CKiMULgRFEQoVIZESMgUhUxCUhJDKCKkMCJJUqACAVLrSDFOhqQKZHAD8AgKlLm4AQBAEoXS5FVwiI6S33lcERRFyB17iauPGjSNGjAgLCwOAt99+OzEx8ccff6x15A7ZP5PJlJJbxQFwHBeo4H08XHmeNxhNgINxd0NSFEFSuurqTRdNMpnMYjL1CARfH28AkADnolICAEmSUil+63BU9foTlp2d3b59e2E7OjrabDYXFhZGRETU7NCyZUvrH8SYmJjs7GwAyMrKGjt2bM1GjuNIsq7l0koL8mid2mQyFefdMFbrOMZi0lZyDMOYjSZtJfC8uVrLUQQPvElbSZtNHEubtJUMQzNmk0lbyXOcpVpn1FYCgElbaTEaOJYxaStZ2sJZTCZtJcdyFmO1SVsJwJv0VRaDjuc4k7aStZhZ2mLSVnIcy5gMJm0lz/Pm6iqeNvM8b9JWMmYjx9AmbSV7+7mA5y3VOpNCcSuM0Wh9LsJiNmkreZaljdUmbSXPg0mnsRh0PMeatJWMxcRx5K3XZX0uvfb/27vzsCauvQ/gJxkmCySBBAIJyCIKCAWqYkVflyogVnstChWFUn1tudU+bn2rvq22Vq9LpY/30fbaXlus5qm1LhWt+lRs9dH2DXWhplI3wA2VVdYQSDIzmcyc94+xKSWAsYUkeM/n4Y/k5MfkG2bhJJkzx2puAxCSbXra0vG5CK7AYm4nMR4EgGzT06TtuSg+TZFteghZ2mwk2/QAAKJdbyGM7MPnoviYGBeKAR9YhNIWZdT5dlziN4LAQn5uKXsuYUnZD0f0htb/SvvvX7/8ICQiNiYq8tbXWwf6yyU8xtTaEjV0lLX+LmhvDpDL+cZmb4wR8Vk+beEDls9YAGOhH/Tcu+h2g9M/1q8BAHl8rrcBIeTGdPF4fL5YYnsrQ1EWPp8PAQQ8Hu4lZVkWQohhGEVRLIQ8Ho9hGC9PTwCAhWFwTymEEPvb30Ni4h8ziKMqKirGjx/P3Y6KijKZTPX19UFBQd3VW63WmpoarocNAJBIJP7+6LpeTkIQBLcVsSwrFosBAG1Gc53RAgAwm0zHq4W4WEqTZsbc6iERAQiZVkIcxADu8gwsC1kGsiyED28AAH9rgZBluKdgWYbH48GHDzEQQsDVMwyAELIMyzAAAFs9ZBnIAxCwD5cPWcBC7ga3WNihHkL48A29LQ+EXAyW7bxYWx7IMizL8myxbYv9LTa0xYCQe3UAQm75LMs8jPHH5bMMw+PxaCtbYfEW4RKjqeF6mcVLZrVaSB9o9PSSAQBUoPXpMCUAAAdsmL8Pn8+naZr97eIWOI6jLoU7c6jTYDAYvLwevhfEcVwoFLa2tnYsaGtr63iygkQi4Qra2tpsvyiRSGiaJgjC1mLP2tZ87L2XAYRWmty/9ILK3+/p4cMprUaNmaV1Okp7M9Qb97h8lMfnh8kwSqvxaTNAayul1ajZFrzpCqWtHuAFROXfW+8KB/l5UVqNxGQKwgyUVhNgecDSjZRWEyS2Siv+j6rXDfSTsOe+EtFUsIiitBrf9kaJhaa0mkDMJK0uptrKQn0E/EuHAQChUh6l1fi06vmWdkqrUQG9qOFXSns/WMoXlX7H4h7hCjGl1UiMxiCegdJqAuh6oG+htI2BIqvkzg9UXfEgpdR69ksxRYYISUqrUZoaLAxDaTVqAelddZ5qvRYmF/F+KfBg2VAvSGk1Cn0LTpkprUYN2sT1JZT2brCUL7h2HHp4hMuFlFYja28LZFsorUZlbeI3GyntgyAx63X7DFV9bpBSRv2fxpMkBuAmSqvxJ+qtEFBaTSBukd3/iWr+NUwuBj9/LWCswWIrpdX4GppFBElpNTIeYW28dd/SUMmX8GShGJ9/60F5dRvPSPu2EPwQ/7BaI46LPJVK5d1bNwcEB0sFHlU3rkVHRtCEmWxpVKtVVGszBoBC5mVqbpBKJJ4CD0NjvZ+vAmNok8molHrSFAVYVirELSThJcREfB5BkAKRUMgyNE3jOM6HVgwyPD4fsiwfACH4/SI5PMgCigAAdBwDzpIm3m8tf/hQgjDYRn394SQac8vDSn0dAKD0+rW+6zR03Pg9PT35fH5ra2sPnYaampoFCxbYvgaOiooqKCjoo2yOM5lM/XrYvSP5IYQ3a5vbLAAAAElDqELC5/Nb2s01FqGHh4fFQo3yIgRCghEwFgEl9moDAJgw1guvBQAQPrRQ3MDn8wlvswdO47iR9rawLCvEKRZjLHxShNcCAEwK1ktQx9ULRE0Yhlm8CYCRAtxkldJWKy3CGYixhA/pydXLGU/hAx6P1yoze3k24bjB4kMCwBPghNXLasUtIrwWekCzwsrFMCvowAdmAECo2Orp1YzjbRZvCrLwtxjEwxh+kKsnFVaBqJHP51M+Zh5mEeAmq4xmrFYhTkOMJQElxmsBAEYfxkv4gMfjkQqLh6DRw8OD8jHz+KQAJ6wSK41TYrwWekBCYfF8GMMiFtXzeDzSh8TwZhxvM0tNDMNKpXyGYWjKKvIkAQCmdsu9xnYAAEYZeYQBwzCjyVxnwXFcAACI9BN7S7v9H+F8/wm7gI1IJHrkp6EOdRr8/f1tvQSCIEiS7PQeSKlUduxG6PV67pyvjr+o1+u9vLx66DEAAGQCcPtSkUKhcCSV+2tubvb19XV1il5jNBo9PDxEIhcNRWcZliT+2ARZwthVJcuSPY5/YxhoIRiGecYvpBcDdtJx4zcYDCzL9vzJQWho6I4dO4YPH953kf4EkiQlkn48OsDB/AlRnYcoDwQgoW8iPZaWFplcLnfkoN/adN5YCuLDAiTPRDghmINIkqRpWip99AjwOCek+VP+Q3YBxzk0sUpcXJxOp+Nu63Q6pVKpUqk6FsTGxpaXlxuNRgAAwzAlJSVxcXFce8df5Bp7YDAYuIU8GV566aWzZ8+6OkWv2bhx42effeayp+djfE/JH3+kHr7qLn6UQYLgiJ5+woYII4cdv3b3f1b8b9/l7bTxq9VqPz+/vnu6vlBaWvq3v/3N1Sn+kri4OIIgHl3nrnJzc0+dOuXqFH9efn7+hg0bXJ3iz7t+/fq0adNcneIv6fVdwKFOw9y5c4uKivbs2VNWVrZq1arXXnuNu+bX0qVLd+7cCQCIiYkZNWrUsmXLbt++/c4776hUqjFjxgAA5s+fv2vXrlOnTpWUlGzatOn111/v+Ym4EZt/+UW5C4qiSJJ0dYpe84S9HJIk+/TlzJs379SpU/v37y8tLX3nnXcWLFjQ7z7k7Os/kROYTKZ+fUjp7zsdSZLc5J/91BOwCxiNRqvV2osLdKjToFKpjh079sUXX8yaNWvs2LHvvfce165QKGyfe+zbt89sNs+YMePOnTvHjh3jjo+JiYmfffbZ2rVrc3NzFy9ePGfOnF6MjiDuLDg4+JtvvtmxY0dWVlZqaurKlStdnQhBEOSvcnQA2LPPPvvss892alyzZo3ttkql+vLLL+1/MTMzMzMz80/nQ5D+Kzk5OTk52dUpEARBeo3bjRrfv3+/Uql0dYreUVtbe/z48Tt37rg6SO+4evXq/fv38/PzXR2kd1y4cMFgMLg6xe+MRuPhw4dtp0G4g8rKyubm5n69xrkL1Lrs7N2/rLKy8vvvv3/w4MEjK6Prrw4E4Pz583dvNjkhmIOKi4sNBkP/3YTu37//BOwCGo3GwV3gmWeeGTZsWM817tVpGDhwYEVFRWVlpauD9I6AgICGhgaT6QmZxAXHcZZlf/nlF1cH6R0mkyk6OtrVKX4XHx9fXV3d2Njo6iC/oygqJCSkX6/x2NjYa9eu9buzSWz8/Pz0er0jq6AUMEJeIHG/lbrnRuuLZVmBQNB/NyGSJIODg/tvfgBAXFyc47uAl5fXIzsNPHSNTwRBEARBHOHQiZAIgiAIgiCo04AgCIIgiENQpwFBEARBEIegTgOCIAiCIA5BnQYEQRAEQRzisiGXNE3rdDqRSDR06NDuRoOUlZU1NTUlJCR0nELTPTU3N5eVlXl7ez/11FNdzv3NzRXOkclk7jwNAUEQdXV1trsBAQFdTjPW0NBQWloaGRkZGBjoxHSPrdPLAQCo1Wpu+mOb+vp628hYDMNCQ0Odl89dVVZWVlRUxMfHdzeBXGNjY3l5uZ+fn1uNXLUxGo2XLl1SqVSRkZH2j9bV1XW8IL9QKOxhAlKXoChKp9NJpdL4+G4nYm1ra7t8+bKnp+fTTz/9yMkJne/GjRv19fUJCQldHkDu3btnmw7bPSeCv3PnTnV19bBhw2QyWQ9lFRUVcrlcLpc7LZiD2traSkpKgoKCBg8e3GXB7du3a2pqFApFd/+2ugZdoba2NjIycvTo0TExMUlJSdxk9h2xLJuTkxMaGjpx4sTAwMBr1665JKeD3n77bblcPmbMmMGDB8fFxdXW1trX8Pn80NDQ8PDw8PDwd9991/khHXf69GmBQBD+m8LCQvuavXv3+vr6Tp482c/Pb/v27c4P6TitVmt7LcHBwQCAixcvdqrJzMz08/PjaoYPH+6SnG5l48aNSqUyNTXV19e3yw1g27Ztvr6+aWlpQ4YMGT9+vMlkcn7IHuh0OpVKlZycHBwcPH/+fPuC7Oxs21YhlUpTUlKcH7IHFRUVoaGh48aNi4iIeOGFF2iatq/Zs2ePQqFITEwcMWJEbm6u80P27NVXXw0ODk5KSlKr1SUlJfYFCoUiODiYWwWLFy92fsKeLV++XK1Wp6SkKJXKn376qbsyjUbD4/HWrl3rzGyOOHfunL+/f0pKSlBQ0BtvvGFfsGTJkkGDBiUlJQ0aNCg2NrbLf1tdck2n4Y033sjOzoYQWiyWhISEzz//vFPBmTNngoKC9Ho9hHD16tVpaWkuSOmw8+fPcwdNhmGmTp26cOFC+xo+n9/Y2Oj0aH/G6dOnhw4d2kMBRVH+/v4nT56EEP7yyy9SqdRgMDgr3V+i0WgiIyNZlu3UnpmZ6eZdH2eqqakRi8U3b96EEO7fvz8iIqLTX8xqtXp6ep4+fRpCSNN0ZGTk7t27XZO1GykpKZs2bYIQNjU1+fv7FxcX91AcHR2t0WiclMwx8+bNe/311yGEZrN5yJAhBw8e7FRw/fp1iUSi0+m4uyRJOjtij86ePRsQENDU1AQh3LBhw3PPPWdfo1Aobt265fRoDiktLfX29q6pqYEQfvLJJ4mJiV2W1dbWxsTETJo0yQ07DWPGjPnwww8hhA8ePJDL5VeuXOlUYDabuRssy6ampr711lsOLtk15zQUFBTMnTsXAIDjeHZ2dkFBgX3B9OnTfXx8AABz58799ttv3Xl+21GjRnFfoPD5/KFDhzY1dX0Z19ra2o6fyLkzlmVv3rzZ3dUJtVotjuMpKSkAgOHDh4eFhX333XfODfgn7dq1Kzc3t8uvw9rb28vLy/v7jHa94siRI4mJiREREQCA9PT0urq6y5cvd6rBMMzb2xsA4OHh4eXl5Vafjbe0tJw+fZqbHs/X1/f555+3P8LYnDt3rqqq6sUXX3RiwEezHSHFYnFmZqZ9/i+++GLGjBnx8fG3b9+maVooFLoiZrcKCgqmTZvm6+sLAJg7d+7Jkye7vGR7fX39nTt3GIZxesBHOHjwYEpKCvfFa05Ojk6nq6qqsi9buHDhxo0buf9TbqW2tvbcuXPcLhAQEDB58mT7Tcj2FS2Px/Pz8+NmrnaECzoNDMPU1dWFhYVxd8PCwuzXR1VVle175dDQUJZla2trnRnyz9Hr9Xv27Jk5c6b9QziOZ2VljR07Niws7Mcff3R6tMdz7969jIyMyMjIcePG1dTUdHq0srIyNDTU9q83LCysX1z5+9atWxcuXMjJyeny0Y8//jg9PV2hUKxfv97JwdxNVVWVbffEcTwoKKjT+sUwbNeuXYsWLVq+fPkLL7wwbNiwjIwMFwTtRnV1NY7jtlNtujzC2OzcuTMrK8s2W687aG1tbW9vtx0Au8x/8+ZNvV4fHR2dnZ09YMAAd+u1dzyABwUFYRhWXV3dqQbDsNzc3OTk5AEDBhQWFjo9Y0867gIymUwul9sf4vbu3Yth2PTp050dzgFVVVVcbO5ud7tAcXHx/Pnzp0yZ0t7evmzZMgcX7oL3BxRFMQwjEAi4u0Kh0P5TBIIgbAUYhmEY5s6fNHAoipo9e3ZSUlKXB9Da2lruhLItW7bMmjWrsrLS3d4c2IwcObKhoYFbLzk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に合同なのでその体積は $(r-a)^{n-1}/(n-1)!$ に等しい. ゆえに, $x_1\\geqq a$ となる確率は $P(x_1\\geqq a)$ は\n", "\n", "$$\n", "P(x_1\\geqq a) = \\frac{(r-a)^{n-1}/(n-1)!}{r^{n-1}/(n-1)!} = \\left(1-\\frac{a}{r}\\right)^{n-1}\n", "$$\n", "\n", "となるので, $r=n$ のとき, $n\\to\\infty$ で\n", "\n", "$$\n", "P(x_1\\geqq a) = \\left(1-\\frac{a}{n}\\right)^{n-1} \\to \\exp(-a).\n", "$$\n", "\n", "一方, 確率密度函数 $\\exp(-x)$ において $x\\geqq a$ となる確率は\n", "\n", "$$\n", "\\int_a^\\infty \\exp(-x)\\,dx = [-\\exp(-x)]_a^\\infty = \\exp(-a).\n", "$$\n", "\n", "以上を比較することによって, $D^{n-1}(n)$ 上の一様分布に関する $x_1$ の分布は $n\\to\\infty$ で確率密度函数 $\\exp(-x)$ の指数分布に近付くことがわかる. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**注意:** 以上の議論において $D^{n-1}(r)$ に射影したことは本質的ではなく, $\\Delta^{n-1}(r)$ の体積(面積)が $r^{n-1}$ に比例することだけを使っても同様の議論を遂行できる. $D^{n-1}(r)$ に射影するメリットは比例定数が $1/(n-1)!$ になることが易しく求まることに過ぎない. その比例定数は確率を求めるときに分子分母でキャンセルして消えるので議論の本質には何も影響しない. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $D^1(r)$, $D^2(r)$, $D^3(r)$ を図示し, それぞれの長さ, 面積, 体積がそれぞれ $r$, $r^2/2$, $r^3/6$ であることを確認せよ. $\\QED$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = 0:0.01:1\n", "y = 0:0.01:1\n", "f(x,y) = ifelse(x+y>1, NaN, 1-x-y)\n", "\n", "pyplot()\n", "p = plot(size=(350, 300), zlims=(0,1))\n", "surface!(x, y, f, color=:rainbow, camera=(120, 45))\n", "display(p)\n", "gr();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ζ(s) - 1/(s-1) の s→0 での極限がEuler定数に等しいこと\n", "\n", "以下ではこの先に進まないと知らないはずのことを勝手に用いる." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $h>0$ のとき\n", "\n", "$$\n", "\\sum_{n=1}^\\infty \\left(\\frac{1}{n^h}-\\frac{1}{(n+1)^h}\\right) = 1.\n", "$$\n", "\n", "となることを示せ. $\\QED$\n", "\n", "解答略." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $h>0$ ならば, $n\\to\\infty$ で\n", "\n", "$$\n", "\\frac{1}{n^{1+h}} - \\frac{1}{h}\\left(\\frac{1}{n^h} + \\frac{1}{(n+1)^h}\\right) = \n", "O\\left(\\frac{1}{n^{2+h}}\\right)\n", "$$\n", "\n", "となることを示せ.\n", "\n", "**解答例:** 二項展開より\n", "\n", "$$\n", "\\left(1+\\frac{1}{n}\\right)^{-h} = 1 -\\frac{h}{n} + \\frac{h(h+1)}{2n^2} + \\cdots =\n", "1 -\\frac{h}{n} + O\\left(\\frac{1}{n^2}\\right)\n", "$$\n", "\n", "なので\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{(左辺)} &= \n", "\\frac{1}{hn^h}\\left(\\frac{h}{n} - 1 + \\left(1+\\frac{1}{n}\\right)^{-h}\\right) \n", "\\\\ &=\n", "\\frac{1}{hn^h}\\left(\\frac{h}{n} - 1 + 1 - \\frac{h}{n} + O\\left(\\frac{1}{n^2}\\right)\\right) =\n", "O\\left(\\frac{1}{n^{2+h}}\\right).\n", "\\qquad\\QED\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**定義:** $s>1$ に対して, $\\zeta(s)$ を\n", "\n", "$$\n", "\\zeta(s) = \\sum_{n=1}^\\infty \\frac{1}{n^s}\n", "$$\n", "\n", "と定める. この級数は絶対収束している." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $h>0$ ならば\n", "\n", "$$\n", "\\zeta(1+h) - \\frac{1}{h} = \n", "\\sum_{k=0}^\\infty\\frac{(-h)^k}{k!}\\gamma_k, \\quad\n", "\\gamma_k = \\sum_{n=1}^\\infty\\left(\\frac{(\\log n)^k}{n} + \\frac{(\\log n)^{k+1}-(\\log(n+1))^{k+1}}{k+1}\\right)\n", "$$\n", "\n", "となることを示せ. $\\QED$\n", "\n", "解答略. \n", "\n", "**ヒント:** この問題の左辺は上の問題の左辺の $n$ に関する総和に等しい. $1/n^h=\\exp(-h\\log n)$ と $1/(n+1)^h=\\exp(-h\\log(n+1))$ に $\\ds\\exp(x)=\\sum_{k=1}^\\infty \\frac{x^k}{k!}$ を適用し, $-h$ に関する同次の項をまとめて整理せよ. そのとき $1/n^{1+h}$ は $\\exp(-h\\log n)/n$ だとみなせ. $\\QED$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** 上の問題の $\\gamma_0$ がEulerの定数 $\\gamma$ に等しいことを示せ.\n", "\n", "**解答例:** \n", "\n", "$$\n", "\\begin{aligned}\n", "\\gamma_0 &=\n", "\\sum_{n=1}^\\infty\\left(\\frac{1}{n} + \\log n - \\log(n+1) \\right) \n", "\\\\ &=\n", "\\left(\\frac{1}{1} - \\log 2\\right) +\n", "\\left(\\frac{1}{2} + \\log 2 - \\log 3 \\right) +\n", "\\left(\\frac{1}{3} + \\log 3 - \\log 4 \\right) + \\cdots\n", "\\end{aligned}\n", "$$\n", "\n", "であり, この級数の $n=N$ までの和は\n", "\n", "$$\n", "\\frac{1}{1} + \\frac{1}{2} + \\cdots + \\frac{1}{N} - \\log(N+1)\n", "$$\n", "\n", "に等しいので, その級数はEuler定数 $\\gamma$ に収束する. $\\QED$\n", "\n", "以上によって\n", "\n", "$$\n", "\\zeta(1+h) = \\frac{1}{h} + \\gamma + O(h) \\quad(h\\to 0)\n", "$$\n", "\n", "であることが示された." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $\\ds\n", "\\zeta(1+h) = \\frac{1}{h} + \\gamma + O(h)\n", "$ ($h\\to 0$) を以上とは別の方法を使って示してみよ. $\\QED$\n", "\n", "例えばEuler-Maclaurinの和公式を使っても証明可能である." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**問題:** $h\\searrow 0$ のとき, $\\ds\\zeta(1+h) - \\frac{1}{h} \\to \\gamma$ となることを数値的に確認せよ. $\\QED$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h = big\"0.1\" ^ N = 1.000000000000000000000000000000000000000000000000000000000000000000000000000053e-25\n", "c = zeta(1 + h) - 1 / h = 0.5772156649015328606065120977128413450763009749950989988242121323324325714408041\n", "g = big(eulergamma) = 0.5772156649015328606065120900824024310421593359399235988057672348848677267776685\n", "round(c, digits = N) = 0.5772156649015328606065121000000000000000000000000000000000000000000000000000015\n", "round(g, digits = N) = 0.5772156649015328606065121000000000000000000000000000000000000000000000000000015\n", "c - g = 7.630438914034141639055175400018444897447564844663135574900855315781988976401014e-27\n" ] } ], "source": [ "N = 25\n", "@show h = big\"0.1\"^N\n", "@show c = zeta(1+h)-1/h\n", "@show g = big(eulergamma)\n", "@show round(c, digits=N)\n", "@show round(g, digits=N)\n", "@show c - g;" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5772156649015328606065120900824024310421593359399235988057672348848677267776685" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BigFloat(eulergamma)" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "_draft": { "nbviewer_url": "https://gist.github.com/0da54b1e114e79f0c55c1b1bc07e9cb8" }, "gist": { "data": { "description": "03 pi, e, and Euler's γ", "public": true }, "id": "0da54b1e114e79f0c55c1b1bc07e9cb8" }, "jupytext": { "formats": "ipynb,md" }, "kernelspec": { "display_name": "Julia 1.9.1", "language": "julia", "name": "julia-1.9" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.1" }, "toc": { "base_numbering": 1, "nav_menu": { "height": "207px", "width": "242px" }, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "目次", "title_sidebar": "目次", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "214px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }