{"id":34086,"date":"2021-03-27T13:00:31","date_gmt":"2021-03-27T13:00:31","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34086"},"modified":"2025-08-16T06:39:54","modified_gmt":"2025-08-16T06:39:54","slug":"%e3%82%b9%e3%82%bf%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ae%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ja\/%e3%82%b9%e3%82%bf%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%ae%e5%85%ac%e5%bc%8f\/","title":{"rendered":"\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f<\/h1>\n<p><em>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306f\u3001\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u8a08\u7b97\u3092\u7c21\u7565\u5316\u3059\u308b\u305f\u3081\u306e\u4e0d\u53ef\u6b20\u306a\u9053\u5177\u3067\u3042\u308a\u3001\u8fc5\u901f\u304b\u3064\u5b9f\u7528\u7684\u306a\u304a\u304a\u3088\u305d\u3092\u4e0e\u3048\u308b\u3082\u306e\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u306e\u7d50\u679c\u306f\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u3092\u6271\u3046\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u71b1\u529b\u5b66\u3001\u78ba\u7387\u8ad6\u3001\u6f38\u8fd1\u89e3\u6790\u3068\u3044\u3063\u305f\u5206\u91ce\u306b\u304a\u3044\u3066\u7279\u306b\u6709\u7528\u3067\u3042\u308b\u3002\u305d\u306e\u5c55\u958b\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306f\u3001\u305d\u306e\u5fdc\u7528\u3092\u5bb9\u6613\u306b\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u52b9\u7387\u7684\u306a\u8a08\u7b97\u3084\u8907\u96d1\u306a\u554f\u984c\u89e3\u6c7a\u306b\u304a\u3051\u308b\u305d\u306e\u91cd\u8981\u6027\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306b\u3082\u3064\u306a\u304c\u308b\u3002<br \/>\n<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19:<\/strong><br \/>\n\u672c\u8b1b\u7fa9\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u30ac\u30f3\u30de\u95a2\u6570\u306b\u3088\u308b\u968e\u4e57\u306e\u5b9a\u7fa9\u304b\u3089\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3059\u308b\u3002<\/li>\n<li><strong>\u5fdc\u7528\u3059\u308b<\/strong>\uff1a\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3092\u7528\u3044\u3066\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8fd1\u4f3c\u3059\u308b\u3002<\/li>\n<li><strong>\u8a08\u7b97\u3059\u308b<\/strong>\uff1a\u5bfe\u6570\u3068\u6307\u6570\u306e\u57fa\u672c\u7684\u306a\u9053\u5177\u3092\u7528\u3044\u3066\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u884c\u3046\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u76ee\u6b21<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u8a3c\u660e<\/a><br \/>\n<a href=\"#2\">\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c<\/a><br \/>\n<a href=\"#3\">\u4f8b\uff1a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306e\u8fd1\u4f3c<\/a>\n<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u8a3c\u660e<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/CcHCyRR1WrY?si=eTZsj4wBqQ2krELG\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u5c55\u958b\u306f\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306b\u3088\u308b\u968e\u4e57\u306e\u5b9a\u7fa9\u304b\u3089\u59cb\u307e\u308b\u3002\u305d\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">n! =\\Gamma(n+1) = \\displaystyle \\int_0^\\infty t^n e^{-t} \\, dt<\/span>\n<p>\u3053\u306e\u5f0f\u3092\u7528\u3044\u3066\u5909\u6570\u5909\u63db\u3092\u884c\u3046\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">t = nx<\/span>\u3002\u3053\u308c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">x \\in [0, \\infty[<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">dt = n dx<\/span> \u3092\u610f\u5473\u3059\u308b\u3002\u3053\u306e\u5909\u63db\u306b\u3088\u308a\u3001\u7a4d\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3055\u308c\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">n! = \\Gamma(n+1) = \\displaystyle \\int_0^\\infty (nx)^n e^{-nx} n \\, dx = n^{n+1} \\int_0^\\infty x^n e^{-nx} dx<\/span>\n<p>\u6b21\u306b\u3001\u4e8c\u5ea6\u76ee\u306e\u5909\u6570\u5909\u63db\u3092\u884c\u3046\uff1a<span class=\"katex-eq\" data-katex-display=\"false\">x = 1 + \\dfrac{s}{\\sqrt{n}}<\/span>\u3002\u3053\u308c\u306b\u3088\u308a\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n &amp; s = (x-1)\\sqrt{n}, \\quad s \\in [-\\sqrt{n}, \\infty[ \\\\ \\\\\n\n &amp; dx = \\dfrac{ds}{\\sqrt{n}}\n\n\\end{array}<\/span>\n<p>\u3053\u306e\u5909\u63db\u3092\u7528\u3044\u308b\u3068\u3001\u7a4d\u5206\u306f\u6b21\u306e\u5f62\u3092\u53d6\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nn! = \\Gamma(n+1) &amp;= \\displaystyle n^{n+1} \\int_{-\\sqrt{n}}^\\infty \\left( 1 + \\dfrac{s}{\\sqrt{n}} \\right)^n e^{-n\\left(1+\\dfrac{s}{\\sqrt{n}}\\right)} \\dfrac{ds}{\\sqrt{n}} \\\\ \\\\\n\n&amp;= \\displaystyle \\dfrac{n^{n+1}}{\\sqrt{n}} \\int_{-\\sqrt{n}}^\\infty e^{n\\ln\\left( 1 + \\dfrac{s}{\\sqrt{n}} \\right)} e^{-n - s\\sqrt{n}} ds \\\\ \\\\\n\n&amp;= \\displaystyle n^n e^{-n} \\sqrt{n} \\int_{-\\sqrt{n}}^\\infty e^{n\\ln\\left(1+\\dfrac{s}{\\sqrt{n}}\\right) - s\\sqrt{n}} ds\n\n\\end{array}\n\n<\/span>\n<p>\u3053\u3053\u3067\u81ea\u7136\u5bfe\u6570\u306e\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u5c55\u958b\u3092\u7528\u3044\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(1+x) = \\displaystyle\\sum_{k=1}^{\\infty} \\dfrac{(-1)^{k+1}x^k}{k}   <\/span>\n<p>\u3053\u306e\u5c55\u958b\u3092 <span class=\"katex-eq\" data-katex-display=\"false\">\\ln\\left(1+\\dfrac{s}{\\sqrt{n}}\\right)<\/span> \u306b\u9069\u7528\u3059\u308b\u3068\u3001\u6307\u6570\u95a2\u6570\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u5c55\u958b\u3055\u308c\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nn\\ln\\left(1+\\dfrac{s}{\\sqrt{n}}\\right) - s\\sqrt{n} &amp; = \\displaystyle n \\left[\\sum_{k=1}^{\\infty} \\dfrac{(-1)^{k+1}\\left(\\dfrac{s}{\\sqrt{n}} \\right)^k}{k} \\right] - s\\sqrt{n} \\\\ \\\\\n\n&amp; = n \\left[ \\dfrac{s}{\\sqrt{n}} - \\dfrac{s^2}{2n} + \\dfrac{s^3}{3n\\sqrt{n}} - \\dfrac{s^4}{4n^2} + \\dfrac{s^5}{5n^2\\sqrt{n}} \\cdots \\right] - s\\sqrt{n} \\\\ \\\\\n\n&amp; = s\\sqrt{n} - \\dfrac{s^2}{2} + \\dfrac{s^3}{3\\sqrt{n}} - \\dfrac{s^4}{4n} + \\dfrac{s^5}{5n\\sqrt{n}} \\cdots - s\\sqrt{n} \\\\ \\\\\n\n&amp; = - \\dfrac{s^2}{2} + \\dfrac{s^3}{3\\sqrt{n}} - \\dfrac{s^4}{4n} + \\dfrac{s^5}{5n\\sqrt{n}} \\cdots \\\\ \\\\\n\n&amp; = - \\dfrac{s^2}{2} + \\displaystyle \\sum_{k=3}^\\infty \\dfrac{(-1)^{k+1}s^k}{k\\sqrt{n^{k-2}}}\n\n\\end{array}\n\n<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5b8c\u5168\u306a\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">n! = \\Gamma(n+1) = \\displaystyle n^n e^{-n} \\sqrt{n} \\int_{-\\sqrt{n}}^\\infty e^{- \\dfrac{s^2}{2} + \\displaystyle \\sum_{k=3}^\\infty \\dfrac{(-1)^{k+1}s^k}{k\\sqrt{n^{k-2}}}} ds <\/span>\n<p>\u3053\u306e\u7d50\u679c\u306f\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u57fa\u672c\u7684\u306a\u3082\u306e\u3067\u3042\u308b\u3002<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3001\u6307\u6570\u306e\u4e2d\u306e\u7dcf\u548c\u9805\u306f 0 \u306b\u53ce\u675f\u3057\u3001\u652f\u914d\u7684\u306a\u9805\u306e\u307f\u304c\u6b8b\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u7a4d\u5206\u306f\u5358\u7d14\u5316\u3055\u308c\u3001\u30ac\u30a6\u30b9\u7a4d\u5206\u3068\u3057\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">n! = \\Gamma(n+1) \\approx \\displaystyle n^n e^{-n} \\sqrt{n} \\int_{-\\infty}^\\infty e^{- \\frac{s^2}{2}} ds = n^n e^{-n} \\sqrt{n} \\sqrt{2\\pi} <\/span>\n<p><strong>\u3053\u306e\u7d50\u679c\u306f\u3001\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306b\u5bfe\u3059\u308b\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\uff1a<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{n! \\approx \\sqrt{2\\pi n}\\left(\\dfrac{n}{e}\\right)^{n}}<\/span>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ASifSl6YgTk?si=8rHCOoUbWoiH962o\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u304b\u3089\u76f4\u63a5\u5c0e\u304b\u308c\u308b\u7d50\u679c\u306e\u4e00\u3064\u304c\u3001\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3067\u3042\u308b\u3002\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u81ea\u7136\u5bfe\u6570\u3092\u53d6\u308b\u3068\u3001\u6b21\u3092\u5f97\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\ln(n!) \\approx \\ln\\left( \\sqrt{2n\\pi}\\left(\\dfrac{n}{e}\\right)^{n} \\right) &amp;=&amp; \\dfrac{1}{2}\\ln(2n\\pi) + n\\ln\\left(\\dfrac{n}{e}\\right) \\\\ \\\\\n\n&amp;=&amp;  \\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n \\\\ \\\\\n\n&amp;\\approx &amp; n\\ln(n) - n\n\n\\end{array}<\/span>\n<p>\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u9805 <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{1}{2}\\ln(2n\\pi)<\/span> \u3092\u7121\u8996\u3059\u308b\u8ffd\u52a0\u306e\u8fd1\u4f3c\u304c\u884c\u308f\u308c\u308b\u3002\u3053\u306e\u9805\u306f\u3001<span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u304c\u5927\u304d\u3044\u5024\u306e\u5834\u5408\u3001<span class=\"katex-eq\" data-katex-display=\"false\">n\\ln(n) - n<\/span> \u306b\u6bd4\u3079\u3066\u7121\u8996\u3067\u304d\u308b\u307b\u3069\u5c0f\u3055\u304f\u306a\u308b\u3002<\/p>\n<p>\u3053\u306e\u8fd1\u4f3c\u306e\u59a5\u5f53\u6027\u306f\u3001\u4e21\u8005\u306e\u8868\u73fe\u306e\u9593\u306e\u76f8\u5bfe\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u6b63\u5f53\u5316\u3055\u308c\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n\\text{\u521d\u671f\u8fd1\u4f3c} &amp; = &amp; \\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n \\\\ \\\\\n\n\\text{\u6700\u7d42\u8fd1\u4f3c} &amp; = &amp; n\\ln(n) - n \\\\ \\\\\n\n\\text{\u76f8\u5bfe\u8aa4\u5dee} &amp;=&amp; \\dfrac{\\text{\u6700\u7d42\u8fd1\u4f3c} - \\text{\u521d\u671f\u8fd1\u4f3c}}{\\text{\u521d\u671f\u8fd1\u4f3c}} \\\\ \\\\\n\n&amp;=&amp; \\dfrac{-\\dfrac{1}{2}\\ln(2n\\pi)}{\\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n}\n\n\\end{array}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">n \\to \\infty<\/span> \u306e\u3068\u304d\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle \\lim_{n\\to\\infty} \\text{\u76f8\u5bfe\u8aa4\u5dee} &amp; = \\displaystyle \\lim_{n\\to\\infty} \\dfrac{-\\dfrac{1}{2}\\ln(2n\\pi)}{\\dfrac{1}{2}\\ln(2n\\pi) + n\\ln(n) - n} \\\\ \\\\\n\n&amp; = \\displaystyle \\lim_{n\\to\\infty} \\dfrac{-\\dfrac{1}{2n}}{\\dfrac{1}{2n} + \\ln(n) + 1 - 1} = 0\n\n\\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u8aa4\u5dee\u304c <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u306e\u5927\u304d\u306a\u5024\u306b\u5bfe\u3057\u3066 0 \u306b\u53ce\u675f\u3059\u308b\u305f\u3081\u3001\u6b21\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u5b89\u5fc3\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\ln(n!) \\approx n\\ln(n) - n}<\/span>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u4f8b\uff1a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306e\u8fd1\u4f3c<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/kja9niRWjpg?si=eHkcZYaq0Fgntc3G\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><em>10.000!<\/em> \u306e\u3088\u3046\u306a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u3001\u305d\u306e\u7d50\u679c\u306e\u5927\u304d\u3055\u306e\u305f\u3081\u306b\u901a\u5e38\u306e\u9053\u5177\u3067\u306f\u307b\u3068\u3093\u3069\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u308b\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u7528\u3044\u308c\u3070\u3001\u57fa\u672c\u7684\u306a\u8a08\u7b97\u6a5f\u3067\u3082\u6271\u3048\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<p>\u968e\u4e57\u306e\u5bfe\u6570\u516c\u5f0f\u306f\u6b21\u3092\u4e0e\u3048\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(10.000!) \\approx 10.000 \\ln(10.000) - 10.000<\/span>\n<p>\u81ea\u7136\u5bfe\u6570 (<span class=\"katex-eq\" data-katex-display=\"false\">\\ln<\/span>) \u3092\u5e38\u7528\u5bfe\u6570 (<span class=\"katex-eq\" data-katex-display=\"false\">\\log<\/span>) \u306b\u5909\u63db\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\ln(10.000!) = \\dfrac{\\log(10.000!)}{\\log(e)}<\/span>\n<p>\u3053\u308c\u306f\u6b21\u3092\u610f\u5473\u3059\u308b\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\log(10.000!) \\approx \\log(e) \\cdot (10.000 \\ln(10.000) - 10.000)<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">10.000! \\approx 10^{\\log(e) \\cdot (10.000 \\ln(10.000) - 10.000)} \\approx 10^{35.657,06}<\/span>\n<p>\u3053\u3053\u3067\u6ce8\u76ee\u3059\u3079\u304d\u306f\u3001\u6307\u6570\u306b\u73fe\u308c\u308b\u8868\u73fe\u304c\u307b\u3068\u3093\u3069\u306e\u8a08\u7b97\u6a5f\u3067\u6271\u3048\u308b\u7bc4\u56f2\u306b\u53ce\u307e\u308b\u3068\u3044\u3046\u70b9\u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u6570\u81ea\u4f53\u3092\u8996\u899a\u5316\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u304f\u3066\u3082\u3001\u305d\u306e\u6841\u6570\u304c\u304a\u3088\u305d 35,657 \u6841\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u3088\u3063\u3066\u3001\u4e00\u898b\u4e0d\u53ef\u80fd\u306b\u601d\u3048\u308b\u8a08\u7b97\u304c\u5b9f\u884c\u53ef\u80fd\u306a\u3082\u306e\u3068\u306a\u308b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306f\u3001\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u8a08\u7b97\u3092\u7c21\u7565\u5316\u3059\u308b\u305f\u3081\u306e\u4e0d\u53ef\u6b20\u306a\u9053\u5177\u3067\u3042\u308a\u3001\u8fc5\u901f\u304b\u3064\u5b9f\u7528\u7684\u306a\u304a\u304a\u3088\u305d\u3092\u4e0e\u3048\u308b\u3082\u306e\u3067\u3042\u308b\u3002 \u3053\u306e\u7d50\u679c\u306f\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u3092\u6271\u3046\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3042\u308b\u71b1\u529b\u5b66\u3001\u78ba\u7387\u8ad6\u3001\u6f38\u8fd1\u89e3\u6790\u3068\u3044\u3063\u305f\u5206\u91ce\u306b\u304a\u3044\u3066\u7279\u306b\u6709\u7528\u3067\u3042\u308b\u3002\u305d\u306e\u5c55\u958b\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306f\u3001\u305d\u306e\u5fdc\u7528\u3092\u5bb9\u6613\u306b\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u52b9\u7387\u7684\u306a\u8a08\u7b97\u3084\u8907\u96d1\u306a\u554f\u984c\u89e3\u6c7a\u306b\u304a\u3051\u308b\u305d\u306e\u91cd\u8981\u6027\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306b\u3082\u3064\u306a\u304c\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19: \u672c\u8b1b\u7fa9\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b \u7406\u89e3\u3059\u308b\uff1a\u30ac\u30f3\u30de\u95a2\u6570\u306b\u3088\u308b\u968e\u4e57\u306e\u5b9a\u7fa9\u304b\u3089\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3092\u5c0e\u51fa\u3059\u308b\u3002 \u5fdc\u7528\u3059\u308b\uff1a\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3092\u7528\u3044\u3066\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8fd1\u4f3c\u3059\u308b\u3002 \u8a08\u7b97\u3059\u308b\uff1a\u5bfe\u6570\u3068\u6307\u6570\u306e\u57fa\u672c\u7684\u306a\u9053\u5177\u3092\u7528\u3044\u3066\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u884c\u3046\u3002 \u5185\u5bb9\u76ee\u6b21: \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u8a3c\u660e \u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c \u4f8b\uff1a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306e\u8fd1\u4f3c \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u8a3c\u660e \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u5c55\u958b\u306f\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306b\u3088\u308b\u968e\u4e57\u306e\u5b9a\u7fa9\u304b\u3089\u59cb\u307e\u308b\u3002\u305d\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff1a \u3053\u306e\u5f0f\u3092\u7528\u3044\u3066\u5909\u6570\u5909\u63db\u3092\u884c\u3046\uff1a\u3002\u3053\u308c\u306f \u304a\u3088\u3073 \u3092\u610f\u5473\u3059\u308b\u3002\u3053\u306e\u5909\u63db\u306b\u3088\u308a\u3001\u7a4d\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3055\u308c\u308b\uff1a \u6b21\u306b\u3001\u4e8c\u5ea6\u76ee\u306e\u5909\u6570\u5909\u63db\u3092\u884c\u3046\uff1a\u3002\u3053\u308c\u306b\u3088\u308a\uff1a \u3053\u306e\u5909\u63db\u3092\u7528\u3044\u308b\u3068\u3001\u7a4d\u5206\u306f\u6b21\u306e\u5f62\u3092\u53d6\u308b\uff1a \u3053\u3053\u3067\u81ea\u7136\u5bfe\u6570\u306e\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u5c55\u958b\u3092\u7528\u3044\u308b\uff1a \u3053\u306e\u5c55\u958b\u3092 \u306b\u9069\u7528\u3059\u308b\u3068\u3001\u6307\u6570\u95a2\u6570\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u5c55\u958b\u3055\u308c\u308b\uff1a \u3057\u305f\u304c\u3063\u3066\u3001\u5b8c\u5168\u306a\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff1a \u3053\u306e\u7d50\u679c\u306f\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u57fa\u672c\u7684\u306a\u3082\u306e\u3067\u3042\u308b\u3002 \u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u3001\u6307\u6570\u306e\u4e2d\u306e\u7dcf\u548c\u9805\u306f 0 \u306b\u53ce\u675f\u3057\u3001\u652f\u914d\u7684\u306a\u9805\u306e\u307f\u304c\u6b8b\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u7a4d\u5206\u306f\u5358\u7d14\u5316\u3055\u308c\u3001\u30ac\u30a6\u30b9\u7a4d\u5206\u3068\u3057\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\uff1a \u3053\u306e\u7d50\u679c\u306f\u3001\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306b\u5bfe\u3059\u308b\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u308b\uff1a \u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c \u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u304b\u3089\u76f4\u63a5\u5c0e\u304b\u308c\u308b\u7d50\u679c\u306e\u4e00\u3064\u304c\u3001\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3067\u3042\u308b\u3002\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u306e\u81ea\u7136\u5bfe\u6570\u3092\u53d6\u308b\u3068\u3001\u6b21\u3092\u5f97\u308b\uff1a \u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u9805 \u3092\u7121\u8996\u3059\u308b\u8ffd\u52a0\u306e\u8fd1\u4f3c\u304c\u884c\u308f\u308c\u308b\u3002\u3053\u306e\u9805\u306f\u3001 \u304c\u5927\u304d\u3044\u5024\u306e\u5834\u5408\u3001 \u306b\u6bd4\u3079\u3066\u7121\u8996\u3067\u304d\u308b\u307b\u3069\u5c0f\u3055\u304f\u306a\u308b\u3002 \u3053\u306e\u8fd1\u4f3c\u306e\u59a5\u5f53\u6027\u306f\u3001\u4e21\u8005\u306e\u8868\u73fe\u306e\u9593\u306e\u76f8\u5bfe\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u6b63\u5f53\u5316\u3055\u308c\u308b\uff1a \u306e\u3068\u304d\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\uff1a \u3057\u305f\u304c\u3063\u3066\u3001\u8aa4\u5dee\u304c \u306e\u5927\u304d\u306a\u5024\u306b\u5bfe\u3057\u3066 0 \u306b\u53ce\u675f\u3059\u308b\u305f\u3081\u3001\u6b21\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u5b89\u5fc3\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a \u4f8b\uff1a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u306e\u8fd1\u4f3c 10.000! \u306e\u3088\u3046\u306a\u975e\u5e38\u306b\u5927\u304d\u306a\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u3001\u305d\u306e\u7d50\u679c\u306e\u5927\u304d\u3055\u306e\u305f\u3081\u306b\u901a\u5e38\u306e\u9053\u5177\u3067\u306f\u307b\u3068\u3093\u3069\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u306e\u516c\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u308b\u968e\u4e57\u306e\u5bfe\u6570\u8fd1\u4f3c\u3092\u7528\u3044\u308c\u3070\u3001\u57fa\u672c\u7684\u306a\u8a08\u7b97\u6a5f\u3067\u3082\u6271\u3048\u308b\u3088\u3046\u306b\u306a\u308b\u3002 \u968e\u4e57\u306e\u5bfe\u6570\u516c\u5f0f\u306f\u6b21\u3092\u4e0e\u3048\u308b\uff1a \u81ea\u7136\u5bfe\u6570 () \u3092\u5e38\u7528\u5bfe\u6570 () \u306b\u5909\u63db\u3059\u308b\u306b\u306f\u3001\u6b21\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308b\uff1a \u3053\u308c\u306f\u6b21\u3092\u610f\u5473\u3059\u308b\uff1a \u3057\u305f\u304c\u3063\u3066\uff1a 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