{"id":32104,"date":"2024-03-26T17:54:04","date_gmt":"2024-03-26T17:54:04","guid":{"rendered":"https:\/\/science-hub.click\/%E5%A4%9A%E9%87%8D%E5%AF%BE%E6%95%B0%E9%96%A2%E6%95%B0%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-03-26T17:54:04","modified_gmt":"2024-03-26T17:54:04","slug":"%E5%A4%9A%E9%87%8D%E5%AF%BE%E6%95%B0%E9%96%A2%E6%95%B0%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=32104","title":{"rendered":"\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><p><strong>\u591a\u5bfe\u6570\u95a2\u6570<\/strong>(\u30b8\u30e7\u30f3\u30ad\u30a8\u30fc\u30eb\u95a2\u6570\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u307e\u3059) \u306f\u6ce8\u76ee\u306b\u5024\u3059\u308b\u95a2\u6570\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e<i>s<\/i>\u304a\u3088\u3073 |z|&lt;1 \u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(z) \\equiv \\sum_{k=1}^\\infty {z^k \\over k^s}} $$<\/div><\/dd><\/dl><p>\u30d1\u30e9\u30e1\u30fc\u30bf<i>s<\/i>\u3068\u5f15\u6570<i>z<\/i>\u306f<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u30bb\u30c3\u30c8<\/a><\/span>\u304b\u3089\u5f15\u304d\u7d99\u304c\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathbb{C}\\,} $$<\/div> \u3001\u8907\u7d20\u6570\u306e\u30bb\u30c3\u30c8\u3002\u7279\u6b8a\u306a\u30b1\u30fc\u30b9 s=2 \u304a\u3088\u3073 s=3 \u306f\u3001\u305d\u308c\u305e\u308c 2 \u6b21\u306e\u591a\u5bfe\u6570\u307e\u305f\u306f 2 \u5bfe\u6570\u3001\u304a\u3088\u3073 3 \u6b21\u306e\u591a\u5bfe\u6570\u307e\u305f\u306f 3 \u5bfe\u6570\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u591a\u91cd\u5bfe\u6570\u306f\u3001\u30d5\u30a7\u30eb\u30df \u30c7\u30a3\u30e9\u30c3\u30af\u5206\u5e03\u3068\u30dc\u30fc\u30ba \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u5206\u5e03\u306e\u7a4d\u5206\u306e\u9589\u3058\u305f\u5f62\u306b\u3082\u73fe\u308c\u3001\u30d5\u30a7\u30eb\u30df \u30c7\u30a3\u30e9\u30c3\u30af\u7a4d\u5206\u307e\u305f\u306f\u30dc\u30fc\u30ba \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u7a4d\u5206\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u591a\u91cd\u5bfe\u6570\u306f\u3001\u540c\u69d8\u306e\u8868\u8a18\u3092\u6301\u3064\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u307e\u305f\u306f\u6574\u6570\u5bfe\u6570\u3068\u6df7\u540c\u3057\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002<\/p><p>\u591a\u5bfe\u6570\u306f\u3001\u89e3\u6790\u62e1\u5f35\u30d7\u30ed\u30bb\u30b9\u3067\u8a31\u53ef\u3055\u308c\u308b\u4e0a\u8a18\u306e<span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9<\/a><\/span>\u3088\u308a\u3082\u5927\u304d\u3044<i>z<\/i>\u306e\u9593\u9694\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p><h2><span>\u30d7\u30ed\u30d1\u30c6\u30a3<\/span><\/h2><p><span><a href=\"https:\/\/science-hub.click\/?p=25840\">\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<\/a><\/span><i>s<\/i>\u304c<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6574\u6570<\/a><\/span>\u3067\u3042\u308b\u91cd\u8981\u306a\u5834\u5408\u3001\u305d\u308c\u306f<i>n<\/i> (\u307e\u305f\u306f\u8ca0\u306e\u5834\u5408\u306f<i>-n<\/i> ) \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u591a\u304f\u306e\u5834\u5408\u3001\u5b9a\u7fa9\u3059\u308b\u3068\u4fbf\u5229\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mu = \\ln(z)\\,} $$<\/div>\u3053\u3053\u3067\u3001ln \u306f\u81ea\u7136\u5bfe\u6570\u306e\u4e3b\u679d\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {- \\pi &lt; \\Im(\\mu) \\le \\pi\\,} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e\u3079\u304d\u4e57\u306f\u5358\u4e00\u5024\u3067\u3042\u308b\u3068\u60f3\u5b9a\u3055\u308c\u307e\u3059\u3002 \uff08\u4f8b\u3048\u3070<div class=\"math-formual notranslate\">$$ {z^s = e^{(s \\ln(z))}\\,} $$<\/div> \uff09\u3002<\/p><p>\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<i>s<\/i>\u306b\u5fdc\u3058\u3066\u3001\u591a\u5bfe\u6570\u306f\u8907\u6570\u306e\u5024\u3092\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u591a\u91cd\u5bfe\u6570\u306e\u4e3b\u5206\u5c90\u304c\u9078\u629e\u3055\u308c\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {Li_s(z)\\,} $$<\/div>\u306f\u5b9f\u6570<i>z<\/i>\u306b\u5bfe\u3057\u3066\u5b9f\u6570\u3067\u3059\u3001 <div class=\"math-formual notranslate\">$$ {0 \\le z \\le 1\\,} $$<\/div> z=1 \u304b\u3089 z=1 \u307e\u3067\u306e\u30ab\u30c3\u30c8\u304c\u884c\u308f\u308c\u308b\u6b63\u306e\u5b9f\u8ef8\u3092\u9664\u3044\u3066\u9023\u7d9a\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\infty\\,} $$<\/div>\u30ab\u30c3\u30c8\u30aa\u30d5\u306b\u3088\u3063\u3066\u5b9f\u8ef8\u304c<i>z<\/i>\u306e\u6700\u3082\u4f4e\u3044\u534a\u5e73\u9762\u306b\u914d\u7f6e\u3055\u308c\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u306b\u95a2\u3057\u3066\u306f<div class=\"math-formual notranslate\">$$ {\\mu\\,} $$<\/div> \u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {- \\pi &lt; \\arg(-\\mu) \\le \\pi\\,} $$<\/div> \u3002\u591a\u91cd\u5bfe\u6570\u304c\u4e0d\u9023\u7d9a\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f<div class=\"math-formual notranslate\">$$ {\\mu\\,} $$<\/div>\u6df7\u4e71\u3092\u5f15\u304d\u8d77\u3053\u3059\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p><p>\u5b9f\u969b\u306e<i>z<\/i>\u3068<div class=\"math-formual notranslate\">$$ {z \\ge 1\\,} $$<\/div> \u3001\u591a\u91cd\u5bfe\u6570\u306e\u865a\u6570\u90e8\u306f (Wood) \u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\textrm{Im}(Li_s(z)) = -{{\\pi \\mu^{s-1}}\\over{\\Gamma(s)}}} $$<\/div><\/dd><\/dl><p>\u30ab\u30c3\u30c8\u3092\u8d8a\u3048\u308b: <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{\\delta\\rightarrow 0^+}\\textrm{Im}(Li_s(z+i\\delta)) = {{\\pi \\mu^{s-1}}\\over{\\Gamma(s)}}} $$<\/div><\/dd><\/dl><p>\u591a\u91cd\u5bfe\u6570\u306e\u5c0e\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {z{\\partial Li_s(z) \\over \\partial z} = Li_{s-1}(z)} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {{\\partial Li_s(e^\\mu) \\over \\partial \\mu} = Li_{s-1}(e^\\mu)} $$<\/div><\/dd><\/dl><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/9FcpOfA4LEw\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2><span>\u7279\u5225\u306a\u5024<\/span><\/h2><p>\u4ee5\u4e0b\u306e\u300c #\u4ed6\u306e\u95a2\u6570\u3068\u306e\u95a2\u4fc2\u300d\u30bb\u30af\u30b7\u30e7\u30f3\u3082\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p><p> <i>s<\/i>\u306e\u6574\u6570\u5024\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u660e\u793a\u7684\u306a\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {Li_{1}(z)  = -\\textrm{ln}\\left(1-z\\right)} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{0}(z)  = {z \\over 1-z}} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{-1}(z) = {z \\over (1-z)^2}} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{-2}(z) = {z(1+z) \\over (1-z)^3}} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{-3}(z) = {z(1+4z+z^2) \\over (1-z)^4}} $$<\/div><\/dd><\/dl><p> <i>s<\/i>\u306e\u3059\u3079\u3066\u306e\u8ca0\u306e\u6574\u6570\u5024\u306b\u5bfe\u3059\u308b\u591a\u5bfe\u6570\u306f\u3001 <i>z<\/i>\u306e\u591a\u9805\u5f0f\u306e\u6bd4\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 (\u4ee5\u4e0b\u306e\u7d1a\u6570\u8868\u73fe\u3092\u53c2\u7167)\u3002\u5f15\u6570\u306e\u534a\u6574\u6570\u5024\u306e\u7279\u6b8a\u306a\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {Li_{1}\\left(1\/2\\right) = \\textrm{ln}(2)} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{2}(1\/2) = {1 \\over 12}[\\pi^2-6(\\ln 2)^2]} $$<\/div><\/dd><dd><div class=\"math-formual notranslate\">$$ {Li_{3}(1\/2) = {1 \\over 24}[4(\\ln 2)^3-2\\pi^2\\ln 2+21\\,\\zeta(3)]} $$<\/div><\/dd><\/dl><p>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\zeta\\,} $$<\/div>\u306f\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3067\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u540c\u69d8\u306e\u516c\u5f0f\u306f\u9ad8\u6b21\u3067\u306f\u77e5\u3089\u308c\u3066\u3044\u307e\u305b\u3093 (Lewin, 1991 p2)\u3002<\/p><h2><span><span><a href=\"https:\/\/science-hub.click\/?p=54391\">\u4ee3\u66ff<\/a><\/span>\u8868\u73fe<\/span><\/h2><ul><li>\u30dc\u30fc\u30ba \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u5206\u5e03\u306e\u7a4d\u5206\u306f\u3001\u591a\u91cd\u5bfe\u6570\u3067\u8868\u3055\u308c\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{s+1}(z) \\equiv {1 \\over \\Gamma(s+1)} \\int_0^\\infty {t^s \\over e^t\/z-1} dt} $$<\/div><\/dd><\/dl>\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u53ce\u675f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\Re(s)  width=} $$<\/div> 0\\\u3001&#8221; &gt;\u3001\u304a\u3088\u3073\u5b9f\u969b\u306e<i>z \u3092<\/i>\u9664\u304f\u3059\u3079\u3066\u306e<i>z<\/i>\u3068<div class=\"math-formual notranslate\">$$ {\\ge 1\\,} $$<\/div> \u3002\u3053\u306e\u6587\u8108\u306b\u304a\u3051\u308b\u591a\u91cd\u5bfe\u6570\u306f\u3001\u30dc\u30fc\u30ba\u7a4d\u5206\u307e\u305f\u306f\u30dc\u30fc\u30b9\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u7a4d\u5206\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/li><li>\u30d5\u30a7\u30eb\u30df \u30c7\u30a3\u30e9\u30c3\u30af\u5206\u5e03\u306e\u7a4d\u5206\u306f\u3001\u591a\u91cd\u5bfe\u6570\u3067\u3082\u8868\u73fe\u3055\u308c\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {-Li_{s+1}(-z) \\equiv {1 \\over \\Gamma(s+1)} \\int_0^\\infty {t^s \\over e^t\/z+1} dt.} $$<\/div><\/dd><\/dl>\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u53ce\u675f\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\Re(s)  width=} $$<\/div> 0\\\u3001&#8221; &gt;\u3001\u304a\u3088\u3073\u5b9f\u6570\u306e<i>z<\/i>\u3068 &lt; -1 \u3092\u9664\u304f\u3059\u3079\u3066\u306e<i>z<\/i> \u3002\u3053\u306e\u6587\u8108\u306b\u304a\u3051\u308b\u591a\u5bfe\u6570\u306f\u3001\u30d5\u30a7\u30eb\u30df\u7a4d\u5206\u307e\u305f\u306f\u30d5\u30a7\u30eb\u30df \u30c7\u30a3\u30e9\u30c3\u30af\u7a4d\u5206\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002(GNU)<\/li><li>\u4ee3\u308f\u308a\u306b\u3001\u591a\u5bfe\u6570\u306f\u4e00\u822c\u306b\u66f2\u7dda\u306e\u30cf\u30f3\u30b1\u30eb\u7a4d\u5206\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 (Whittaker &amp; Watson \u30bb\u30af\u30b7\u30e7\u30f3 12.22\u3001\u30bb\u30af\u30b7\u30e7\u30f3 13.13)\u3002\u30dd\u30fc\u30eb\u304c\u3042\u308b\u9650\u308a<div class=\"math-formual notranslate\">$$ {t=\\mu\\,} $$<\/div>\u88ab\u7a4d\u5206\u95a2\u6570\u306e \u306f\u6b63\u306e\u5b9f\u8ef8\u306b\u63a5\u7d9a\u3055\u308c\u3066\u304a\u3089\u305a\u3001 <div class=\"math-formual notranslate\">$$ {s \\ne 1,2,3\\ldots\\,} $$<\/div> \u3001 \u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059 \uff1a <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^\\mu)={{-\\Gamma(1-s)}\\over{2\\pi i}}\\oint_H {{(-t)^{s-1}}\\over{e^{t-\\mu}-1}}dt} $$<\/div><\/dd><\/dl>\u3053\u3053\u3067\u3001 <i>H \u306f<\/i>\u30cf\u30f3\u30b1\u30eb<span>\u7b49\u9ad8\u7dda<\/span>\u3092\u8868\u3057\u307e\u3059\u3002\u88ab\u7a4d\u5206\u95a2\u6570\u306b\u306f\u5b9f\u8ef8\u306b\u6cbf\u3063\u3066<span><a href=\"https:\/\/science-hub.click\/?p=5522\">0<\/a><\/span>\u304b\u3089<span><a href=\"https:\/\/science-hub.click\/?p=96157\">\u7121\u9650\u5927<\/a><\/span>\u307e\u3067\u306e\u30ab\u30c3\u30c8\u30aa\u30d5\u304c\u3042\u308a\u3001\u5b9f\u8ef8\u306f<span><a href=\"https:\/\/science-hub.click\/?p=59557\">\u30b7\u30fc\u30c8<\/a><\/span>\u306e\u4e0b\u534a\u5206\u306b\u3042\u308a\u307e\u3059 ( <div class=\"math-formual notranslate\">$$ {\\Im(t) \\le 0\\,} $$<\/div> \uff09\u3002\u4e07\u4e00\u306b\u5099\u3048\u3066<div class=\"math-formual notranslate\">$$ {\\mu\\,} $$<\/div>\u304c\u5b9f\u6570\u3067\u6b63\u3067\u3042\u308b\u5834\u5408\u3001\u6975\u306e\u5236\u9650\u5bc4\u4e0e\u3092\u5358\u7d14\u306b\u8ffd\u52a0\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^\\mu)=-{{\\Gamma(1-s)}\\over{2\\pi i}}\\oint_H {{(-t)^{s-1}}\\over{e^{t-\\mu}}-1}dt + 2\\pi i R} $$<\/div><\/dd><\/dl>\u3053\u3053\u3067\u3001 <i>R \u306f<\/i>\u6975\u306e\u5270\u4f59\u3067\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {R = {{\\Gamma(1-s)(-\\mu)^{s-1}}\\over{2\\pi}}} $$<\/div><\/dd><\/dl><\/li><li>\u4e8c\u4e57\u95a2\u4fc2\u306f\u6b21\u306e\u65b9\u7a0b\u5f0f\u304b\u3089\u7c21\u5358\u306b<span><a href=\"https:\/\/science-hub.click\/?p=98747\">\u308f\u304b\u308a\u307e\u3059<\/a><\/span>(Clunie\u3001Schr\u00f6dinger \u3082\u53c2\u7167): <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(-z) + Li_s(z) = 2^{1-s} ~ Li_s(z^2)} $$<\/div><\/dd><\/dl> <span><a href=\"https:\/\/science-hub.click\/?p=80957\">Kummer \u95a2\u6570\u306f<\/a><\/span>\u975e\u5e38\u306b\u3088\u304f\u4f3c\u305f\u91cd\u8907\u516c\u5f0f\u306b\u5f93\u3046\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/li><\/ul><h2><span>\u4ed6\u306e\u6a5f\u80fd\u3068\u306e\u95a2\u4fc2<\/span><\/h2><ul><li>z=1 \u306e\u5834\u5408\u3001\u591a\u5bfe\u6570\u306f\u30ea\u30fc\u30de\u30f3<span>\u30bc\u30fc\u30bf<\/span>\u95a2\u6570\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(1) = \\zeta(s)~~~~~~~~~~~~~(\\textrm{Re}(s) width=} $$<\/div> 1)&#8221; &gt;<\/dd><\/dl><\/li><li>\u591a\u91cd\u5bfe\u6570\u306f<span><a href=\"https:\/\/science-hub.click\/?p=56111\">\u3001\u30c7\u30a3\u30ea\u30af\u30ec \u30a4\u30fc\u30bf\u95a2\u6570<\/a><\/span>\u3068\u30c7\u30a3\u30ea\u30af\u30ec<span><a href=\"https:\/\/science-hub.click\/?p=96903\">\u30d9\u30fc\u30bf<\/a><\/span>\u95a2\u6570\u306b\u30ea\u30f3\u30af\u3055\u308c\u3066\u3044\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(-1) = \\eta\\left(s\\right)} $$<\/div><\/dd><\/dl>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\eta(s)\\,} $$<\/div>\u306f\u30c7\u30a3\u30ea\u30af\u30ec\u306e\u03b7\u95a2\u6570\u3067\u3059\u3002\u7d14\u7c8b\u306a\u865a\u6570\u5f15\u6570\u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(\\pm i) = 2^{-s}\\eta(s)\\pm i \\beta(s)} $$<\/div><\/dd><\/dl>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\beta(s)\\,} $$<\/div>\u306f\u30c7\u30a3\u30ea\u30af\u30ec\u306e\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u3059\u3002<\/li><li>\u591a\u5bfe\u6570\u306f\u30d5\u30a7\u30eb\u30df\u30fb\u30c7\u30a3\u30e9\u30c3\u30af\u7a4d\u5206 (GNU) \u306b\u76f8\u5f53\u3057\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {F_s(\\mu)=-Li_{s+1}(-e^\\mu)\\,} $$<\/div><\/dd><\/dl><\/li><li>\u591a\u91cd\u5bfe\u6570\u306f\u3001\u8d85\u8d8a\u30ec\u30eb\u30d2\u95a2\u6570\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3067\u3059 (Erd\u00e9lyi \u30bb\u30af\u30b7\u30e7\u30f3 1.11-14) <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(z)=z~\\Phi(z,s,1)} $$<\/div><\/dd><\/dl><\/li><li>\u591a\u91cd\u5bfe\u6570\u306f\u3001\u6b21\u306e\u3088\u3046\u306b Hurwitz \u30bc\u30fc\u30bf\u95a2\u6570\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^{2\\pi i x})+(-1)^s Li_s(e^{-2\\pi i x})={(2\\pi i)^s \\over \\Gamma(s)}~\\zeta\\left (1-s,x\\right)} $$<\/div><\/dd><\/dl>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\Gamma(s)\\,} $$<\/div>\u306f\u30aa\u30a4\u30e9\u30fc\u306e\u30ac\u30f3\u30de\u95a2\u6570\u3067\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u5834\u5408\u306b\u6709\u52b9\u3067\u3059<dl><dd><div class=\"math-formual notranslate\">$$ {\\textrm{Re}(s) width=} $$<\/div> 1, \\textrm{Im}(x)\\ge 0, 0 \\le \\textrm{Re}(x) &lt; 1&#8243; &gt;<\/dd><\/dl>\u305d\u3057\u3066\u307e\u305f<dl><dd><div class=\"math-formual notranslate\">$$ {\\textrm{Re}(s) width=} $$<\/div> 1, \\textrm{Im}(x)\\le 0, 0 &lt; \\textrm{Re}(x) \\le 1&#8243; &gt;<\/dd><\/dl> (\u591a\u91cd\u5bfe\u6570\u3068<span>\u5bfe\u6570<\/span>\u306e\u4e3b\u5206\u5c90\u304c\u540c\u6642\u306b\u4f7f\u7528\u3055\u308c\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u30a8\u30eb\u30c7\u30eb\u30a4 \u30bb\u30af\u30b7\u30e7\u30f3 1.11-16 \u306e\u7b49\u4fa1<span><a href=\"https:\/\/science-hub.click\/?p=66517\">\u5f0f\u306f<\/a><\/span>\u6b63\u3057\u304f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044)\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001<span>\u53ce\u675f<\/span><span><a href=\"https:\/\/science-hub.click\/?p=69721\">\u5186<\/a><\/span>|z|=1 \u3092\u8d85\u3048\u305f\u591a\u5bfe\u6570\u306e\u7d1a\u6570\u8868\u73fe\u306e\u89e3\u6790\u7684\u62e1\u5f35\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002<\/li><li> Hurwitz \u306e\u30bc\u30fc\u30bf\u95a2\u6570\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u591a\u9805\u5f0f\u306e\u95a2\u4fc2\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {\\zeta(-n,x)=-{B_{n+1}(x) \\over n+1}} $$<\/div><\/dd><\/dl>\u3053\u308c\u306f\u3001\u3059\u3079\u3066\u306e<i>x<\/i>\u304a\u3088\u3073<i>n<\/i> =0,1,2,3,&#8230; \u306b\u5bfe\u3057\u3066\u5f15\u304d\u7d9a\u304d\u6709\u52b9\u3067\u3059\u3002\u6b21\u306e\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{n}(e^{2\\pi i x})+ (-1)^n Li_{n}(e^{-2\\pi i x})  = -{(2 \\pi i)^n\\over n!} B_n\\left({x}\\right)} $$<\/div><\/dd><\/dl> <i>s<\/i>\u3068<i>x<\/i>\u306b\u306f\u4e0a\u8a18\u3068\u540c\u3058\u5236\u7d04\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002 (Erd\u00e9lyi \u5b97\u6d3e 1.11-18 \u306e\u5bfe\u5fdc\u3059\u308b\u65b9\u7a0b\u5f0f\u306f\u5bfe\u5fdc\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044) \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u8ca0\u306e\u6574\u6570\u5024\u306b\u3064\u3044\u3066\u306f\u3001\u3059\u3079\u3066\u306e<i>z<\/i> (Erd\u00e9lyi \u5b97\u6d3e 1.11-17) \u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{-n}(z)+ (-1)^n Li_{-n}\\left(1\/z\\right)=0~~~~~n=1,2,3\\ldots} $$<\/div><\/dd><\/dl><\/li><li>\u306e\u591a\u5bfe\u6570<div class=\"math-formual notranslate\">$$ {\\mu\\,} $$<\/div>\u7d14\u7c8b\u865a\u6570\u306f\u30af\u30e9\u30a6\u30bc\u30f3\u95a2\u6570\u3067\u8868\u73fe\u3067\u304d\u308b<div class=\"math-formual notranslate\">$$ {Ci_s(\\theta)\\,} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {Si_s(\\theta)\\,} $$<\/div> (Lewin\u30011958 Ch VII \u30bb\u30af\u30b7\u30e7\u30f3 1.4\u3001Abramowitz &amp; Stegun \u30bb\u30af\u30b7\u30e7\u30f3 27.8) <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^{\\pm i \\theta}) = Ci_s(\\theta) \\pm i Si_s(\\theta)} $$<\/div><\/dd><\/dl><\/li><li><span><a href=\"https:\/\/science-hub.click\/?p=35670\">\u9006<\/a><\/span>\u7a4d\u5206\u6b63\u63a5\u95a2\u6570<div class=\"math-formual notranslate\">$$ {Ti_s(z)\\,} $$<\/div> (Lewin\u30011958 Ch VII \u30bb\u30af\u30b7\u30e7\u30f3 1.2) \u306f\u591a\u91cd\u5bfe\u6570\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(\\pm iy)=2^{-s}Li_s(-y^2)\\pm i\\,Ti_s(y)} $$<\/div><\/dd><\/dl><\/li><li><span><a href=\"https:\/\/science-hub.click\/?p=23896\">\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u306e\u30ab\u30a4\u95a2\u6570<\/a><\/span><div class=\"math-formual notranslate\">$$ {\\chi_s(z)\\,} $$<\/div> (Lewin\u30011958 Ch VII \u30bb\u30af\u30b7\u30e7\u30f3 1.1\u3001Boersma) \u306f\u591a\u91cd\u5bfe\u6570\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {\\chi_s(z)={1 \\over 2}~[Li_s(z)-Li_s(-z)]} $$<\/div><\/dd><\/dl><\/li><li>\u591a\u91cd\u5bfe\u6570\u306f\u4e00\u9023\u306e Debye \u95a2\u6570\u3068\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {Z_n(z)\\,} $$<\/div> (\u30a2\u30d6\u30e9\u30e2\u30a6\u30a3\u30c3\u30c4 &amp; \u30b9\u30c6\u30ac\u30f3\u6d3e 27.1) <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{n}(e^\\mu)=\\sum_{k=0}^{n-1}Z_{n-k}(-\\mu){\\mu^k \\over k!}~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl>\u975e\u5e38\u306b\u3088\u304f\u4f3c\u305f\u5f0f\u306f\u3001Debye \u95a2\u6570\u3092\u591a\u91cd\u5bfe\u6570\u306b\u95a2\u9023\u4ed8\u3051\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Z_n(\\mu)=\\sum_{k=0}^{n-1}Li_{n-k}(e^{-\\mu}){\\mu^k \\over k!}~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl><\/li><\/ul><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/_9awjv1a_Uo\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2><span>\u30b7\u30ea\u30fc\u30ba\u8868\u73fe<\/span><\/h2><ul><li>\u591a\u91cd\u5bfe\u6570\u306f\u6b21\u306e\u3079\u304d\u4e57\u306e\u7cfb\u5217\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mu=0\\,} $$<\/div>\u4ee5\u4e0b\u306e\u901a\u308a\uff1a\uff08\u30ed\u30d3\u30f3\u30bd\u30f3\uff09\u3002\u30e1\u30ea\u30f3\u5909\u63db\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {M_s(r) =\\int_0^\\infty \\textrm{Li}_s(fe^{-u})u^{r-1}\\,du ={1 \\over \\Gamma(s)}\\int_0^\\infty\\int_0^\\infty {t^{s-1}u^{r-1} \\over e^{t+u}\/f-1}~dt~du} $$<\/div><\/dd><\/dl>\u5909\u6570 t=ab\u3001u=a(1-b) \u3092\u5909\u66f4\u3059\u308b\u3068\u3001\u7a4d\u5206\u3092\u5206\u96e2\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {M_s(r)={1 \\over \\Gamma(s)}\\int_0^1 b^{r-1} (1-b)^{s-1}db\\int_0^\\infty{a^{s+r-1} \\over e^a\/f-1}da = \\Gamma(r)\\textrm{Li}_{s+r}(f)} $$<\/div><\/dd><\/dl> f=1 \u306e\u5834\u5408\u3001\u9006\u30e1\u30ea\u30f3\u5909\u63db\u306b\u3088\u308a\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{s}(e^{-u})={1 \\over 2\\pi i}\\int_{c-i\\infty}^{c+i\\infty}\\Gamma(r) \\zeta(s+r)u^{-r}dr} $$<\/div><\/dd><\/dl>\u3053\u3053\u3067\u3001 <i>c \u306f<\/i>\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u6975\u306e\u53f3\u5074\u306e\u5b9a\u6570\u3067\u3059\u3002\u7a4d\u5206\u30d1\u30b9\u306f\u9589\u3058\u305f\u8f2a\u90ed\u306b\u5909\u63db\u3067\u304d\u3001\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u6975\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\Gamma(r)\\,} $$<\/div> r=0\u3001-1\u3001-2\u3001&#8230;\u3001\u304a\u3088\u3073<div class=\"math-formual notranslate\">$$ {\\zeta(s+r)\\,} $$<\/div> r=1-s \u3067\u3002\u6b8b\u5dee\u3092\u5408\u8a08\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059<span>\u3002 \u03bc | &lt; 2\u03c0<\/span>\u304a\u3088\u3073<div class=\"math-formual notranslate\">$$ {s \\ne 1,2,3,\\ldots\\,} $$<\/div><dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^\\mu) = \\Gamma(1-s)(-\\mu)^{s-1} + \\sum_{k=0}^\\infty {\\zeta(s-k) \\over k!}~\\mu^k} $$<\/div><\/dd><\/dl>\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<i>s \u304c<\/i>\u6b63\u306e\u6574\u6570<i>n<\/i>\u3067\u3042\u308b\u5834\u5408\u3001\u304a\u3088\u3073 k=n-1 \u9805\u306e\u5834\u5408\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306f\u7121\u9650\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u305d\u308c\u3089\u306e\u5408\u8a08\u306f\u7121\u9650\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6574\u6570 k&gt;0 \u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{s\\rightarrow k+1}\\left[  {\\zeta(s-k)\\mu^k \\over k!}+\\Gamma(1-s)(-\\mu)^{s-1}\\right] = {\\mu^k \\over k!}\\left(\\sum_{m=1}^k{1 \\over m}-\\textrm{Ln}(-\\mu)\\right)} $$<\/div><\/dd><\/dl> k=0\u306e\u5834\u5408: <dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{s\\rightarrow 1}\\left[ \\zeta(s)+\\Gamma(1-s)(-\\mu)^{s-1}\\right] = -\\textrm{Ln}(-\\mu)} $$<\/div><\/dd><\/dl>\u3057\u305f\u304c\u3063\u3066\u3001 <i>s=n<\/i>\u306e\u5834\u5408\u3001 <i>n \u306f<\/i>\u6b63\u306e\u6574\u6570\u3067\u3042\u308a\u3001 <div class=\"math-formual notranslate\">$$ {|\\mu|&lt;2\\pi\\,} $$<\/div> \u3001\u6b21\u306e\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{n}(e^\\mu) = {\\mu^{n-1} \\over (n-1)!}\\left(H_{n-1}-\\textrm{Ln}(-\\mu)\\right) +} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {\\sum_{k=0,k\\ne n-1}^\\infty {\\zeta(n-k) \\over k!}~\\mu^k  ~~~~~~~~~~~~~~~~~~~~~~(n=2,3,4,\\ldots)} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {Li_{1}(e^\\mu) =-\\textrm{Ln}(-\\mu)+ \\sum_{k=1}^\\infty {\\zeta(1-k) \\over k!}~\\mu^k  ~~~~~~~~~~(n=1)} $$<\/div><\/dd><\/dl>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {H_{n-1}\\,} $$<\/div>\u306f\u9ad8\u8abf\u6ce2\u6570\u3067\u3059: <dl><dd><div class=\"math-formual notranslate\">$$ {H_{n-1}\\equiv \\sum_{k=1}^{n-1}{1\\over k}} $$<\/div><\/dd><\/dl>\u7528\u8a9e\u306e\u554f\u984c\u306b\u306f\u6b21\u306e\u3082\u306e\u304c\u542b\u307e\u308c\u307e\u3059<div class=\"math-formual notranslate\">$$ {-ln(-\\mu)\\,} $$<\/div>\u3053\u308c\u3092\u639b\u3051\u308b\u3068<div class=\"math-formual notranslate\">$$ {\\mu^k\\,} $$<\/div>\u6b21\u306e\u5834\u5408\u306f\u30bc\u30ed\u306b\u5411\u304b\u3046\u50be\u5411\u304c\u3042\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mu\\,} $$<\/div> k=0 \u3092\u9664\u304d\u3001\u30bc\u30ed\u306b\u5411\u304b\u3046\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u771f\u306e\u5bfe\u6570\u7279\u7570\u70b9\u304c\u5b58\u5728\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {Li_s(z)\\,} $$<\/div> s=1 \u304a\u3088\u3073 z=1 \u306e\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{\\mu\\rightarrow 0}\\Gamma(1-s)(-\\mu)^{s-1}=0~~~~~(\\textrm{Re}(s) width=} $$<\/div> 1)&#8221; &gt;<\/dd><\/dl>\u30ea\u30fc\u30de\u30f3 \u30bc\u30fc\u30bf\u95a2\u6570\u3068\u30d9\u30eb\u30cc\u30fc\u30a4\u6570\u306e\u95a2\u4fc2\u306e\u4f7f\u7528<div class=\"math-formual notranslate\">$$ {B_k\\,} $$<\/div> : <dl><dd><div class=\"math-formual notranslate\">$$ {\\zeta(-n)=(-1)^n{B_{n+1} \\over n+1}~~~~~~~~~~~(n=0,1,2,3,\\ldots)} $$<\/div><\/dd><\/dl> <i>s<\/i>\u3068<span>|<\/span>\u306e\u8ca0\u306e\u6574\u6570\u5024\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <span>\u03bc | &lt; 2\u03c0<\/span> : <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{-n}(z) =  {n! \\over (-\\mu)^{n+1}}- \\sum_{k=0}^{\\infty} { B_{k+n+1}\\over k!~(k+n+1)}~\\mu^k ~~~~~~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl>\u305d\u308c\u4ee5\u6765\u3001\u4f8b\u5916\u3068\u3057\u3066<div class=\"math-formual notranslate\">$$ {B_1\\,} $$<\/div> \u3001\u3059\u3079\u3066\u306e\u30d9\u30eb\u30cc\u30fc\u30a4\u6570\u306f\u30bc\u30ed\u306b\u7b49\u3057\u3044\u3002\u6b21\u3092\u4f7f\u7528\u3057\u3066\u9805<i>n<\/i> =0 \u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\zeta(0)=B_1=-\\frac{1}{2}\\,} $$<\/div> \u3002 Erd\u00e9lyi \u5b97\u6d3e\u306e\u7b49\u4fa1\u5f0f\u306b\u3082\u3046\u4e00\u5ea6\u6ce8\u76ee\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u591a\u91cd\u5bfe\u6570\u3068\u5bfe\u6570\u306e\u4e3b\u5206\u5c90\u304c\u540c\u6642\u306b\u4f7f\u7528\u3055\u308c\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u30011.11-15 \u306f\u6b63\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002 <div class=\"math-formual notranslate\">$$ {\\ln(\\frac{1}{z})\\,} $$<\/div>\u4e00\u69d8\u306b\u7b49\u3057\u304f\u306a\u3044<div class=\"math-formual notranslate\">$$ {-ln(z)\\,} $$<\/div> \u3002<\/li><li>\u5b9a\u7fa9\u3055\u308c\u305f\u65b9\u7a0b\u5f0f\u306f\u3001\u66f2\u7dda\u30cf\u30f3\u30b1\u30eb\u7a4d\u5206\u3092\u4f7f\u7528\u3057\u3066\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc<i>s<\/i>\u306e\u8ca0\u306e\u5024\u306b\u62e1\u5f35\u3067\u304d\u307e\u3059 (Wood\u3001Gradshteyn &amp; Ryzhik \u30bb\u30af\u30b7\u30e7\u30f3 9.553)\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^\\mu)=-{\\Gamma(1-p) \\over 2\\pi i}\\oint_H{(-t)^{s-1} \\over e^{t-\\mu}-1}dt} $$<\/div><\/dd><\/dl>\u3053\u3053\u3067\u3001 <i>H \u306f<\/i>\u3001 <span><i>t<\/i> \u2212 \u03bc = 2 <i>k<\/i> \u03c0 <i>i<\/i><\/span>\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u6975\u3092\u56f2\u3080\u3088\u3046\u306b\u4fee\u6b63\u3067\u304d\u308b\u30cf\u30f3\u30b1\u30eb\u7b49\u9ad8\u7dda\u3067\u3042\u308a\u3001\u7a4d\u5206\u306f\u6b8b\u5dee\u306e\u5408\u8a08\u3068\u3057\u3066\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_s(e^\\mu)=\\Gamma(1-s)\\sum_{k=-\\infty}^\\infty (2k\\pi i-\\mu)^{s-1}} $$<\/div><\/dd><\/dl>\u3053\u308c\u306f<span>\u3001 Re( <i>s<\/i> ) &lt; 0<\/span>\u304a\u3088\u3073<i>z=1<\/i>\u3092\u9664\u304f\u3059\u3079\u3066\u306e<i>z<\/i>\u306b\u5bfe\u3057\u3066\u5f15\u304d\u7d9a\u304d\u6709\u52b9\u3067\u3059\u3002<\/li><li>\u8ca0\u306e\u6574\u6570<i>s<\/i>\u306e\u5834\u5408\u3001\u591a\u91cd\u5bfe\u6570\u306f\u30aa\u30a4\u30e9\u30fc\u6570\u3092\u542b\u3080\u7d1a\u6570\u3068\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{-n}(z) =   {1 \\over (1-z)^{n+1}} \\sum_{i=0}^{n-1}\\left\\langle{n\\atop i}\\right\\rangle z^{n-i} ~~~~~~~~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\left\\langle{n\\atop i}\\right\\rangle} $$<\/div>\u306f\u30aa\u30a4\u30e9\u30fc\u6570\u3067\u3059\u3002<\/li><li>\u8ca0\u306e\u6574\u6570\u3092\u8868\u3059\u5225\u306e\u660e\u793a\u7684\u306a\u5f0f\u306f (Wood)<i>\u3067\u3059<\/i>\u3002 <dl><dd><div class=\"math-formual notranslate\">$$ {Li_{-n}(z) =   \\sum_{k=1}^{n+1}{(-1)^{n+k+1}(k-1)!S(n+1,k) \\over (1-z)^k} ~~~~~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl>\u3053\u3053\u3067\u3001S(n,k) \u306f\u7b2c 2<span><a href=\"https:\/\/science-hub.click\/?p=93809\">\u7a2e<\/a><\/span>\u30b9\u30bf\u30fc\u30ea\u30f3\u30b0\u6570\u3067\u3059\u3002<\/li><\/ul><h2><span>\u9650\u754c\u3067\u306e\u884c\u52d5<\/span><\/h2><p>\u6b21\u306e\u5236\u9650\u306f\u3001\u591a\u5bfe\u6570 (Wood) \u306b\u5bfe\u3057\u3066\u5f15\u304d\u7d9a\u304d\u6709\u52b9\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{|z|\\rightarrow 0} Li_s(z) = \\lim_{s \\rightarrow \\infty} Li_s(z) = z} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{\\mathrm{Re}(\\mu) \\rightarrow \\infty} Li_s(e^\\mu) = -{\\mu^s \\over \\Gamma(s+1)} ~~~~~~(s\\ne -1, -2,-3,\\ldots)} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{\\mathrm{Re}(\\mu) \\rightarrow \\infty} Li_{n}(e^\\mu) = -(-1)^ne^{-\\mu} ~~~~~~(n=1,2,3,\\ldots)} $$<\/div><\/dd><\/dl><dl><dd><div class=\"math-formual notranslate\">$$ {\\lim_{|\\mu|\\rightarrow 0} Li_s(e^\\mu) =  \\Gamma(1-s)(-\\mu)^s~~~~~~(s&lt;1)} $$<\/div><\/dd><\/dl><h2><span>\u591a\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb<\/span><\/h2><p>Leonard Lewin \u306f\u3001\u7279\u5b9a\u306e\u5024\u306e\u591a\u5bfe\u6570\u306b\u95a2\u3059\u308b\u591a\u6570\u306e\u53e4\u5178\u7684\u306a\u95a2\u4fc2\u306e\u9a5a\u304f\u3079\u304d<span><a href=\"https:\/\/science-hub.click\/?p=7924\">\u4e00\u822c\u5316<\/a><\/span>\u3092\u767a\u898b\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306f\u73fe\u5728\u3001\u591a\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002\u5b9a\u7fa9\u3057\u307e\u3057\u3087\u3046<div class=\"math-formual notranslate\">$$ {\\rho=\\frac{(\\sqrt{5}-1)}{2}\\,} $$<\/div>\u9ec4\u91d1\u6bd4\u306e\u9006\u307f\u305f\u3044\u306b\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b9\u30b1\u30fc\u30eb\u304b\u3089\u306e\u7d50\u679c\u306e 2 \u3064\u306e\u7c21\u5358\u306a\u4f8b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {Li_2(\\rho^6)=4Li_2(\\rho^3)+3Li_2(\\rho^2)-6Li_2(\\rho)+\\frac{7\\pi^2}{30}} $$<\/div><\/dd><\/dl><p> 1935\u5e74\u306b\u30b3\u30af\u30bb\u30bf\u30fc\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u3001 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {Li_2(\\rho)=\\frac{\\pi^2}{10} &#8211; \\log^2\\rho} $$<\/div><\/dd><\/dl><p>\u30e9\u30f3\u30c7\u30f3\u3055\u3093\u304b\u3089\u9802\u304d\u307e\u3057\u305f\u3002\u591a\u91cd\u5bfe\u6570\u30b9\u30b1\u30fc\u30eb\u306f\u3001K \u7406\u8ad6\u306b\u81ea\u7136\u304b\u3064\u6df1\u304f\u73fe\u308c\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/rQXJyesqvhg\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2><span>\u6b74\u53f2<\/span><\/h2><p>\u30c9\u30f3\u30fb\u30b6\u30ae\u30fc\u30eb\u306f\u3001\u300c\u4e8c\u5bfe\u6570\u306f\u30e6\u30fc\u30e2\u30a2\u306e<span><a href=\"https:\/\/science-hub.click\/?p=81037\">\u30bb\u30f3\u30b9<\/a><\/span>\u306e\u3042\u308b\u552f\u4e00\u306e\u6570\u5b66\u95a2\u6570\u3067\u3042\u308b\u300d\u3068\u8ff0\u3079\u307e\u3057\u305f\u3002<\/p><h2><span>\u82f1\u8a9e\u306e\u51fa\u7248\u7269<\/span><\/h2><ul><li>\u30a2\u30d6\u30e9\u30e2\u30a6\u30a3\u30c3\u30c4 M. \u304a\u3088\u3073\u30a2\u30a4\u30aa\u30ef\u5dde\u30b9\u30c6\u30ac\u30f3 (\u7de8)\u3001\u6570\u5b66\u95a2\u6570\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3001\u56fd\u5bb6\u6a19\u6e96\u5c40\u30011964 \u5e74\u3002\u30c9\u30fc\u30d0\u30fc\u51fa\u7248\u30011965 \u5e74\u306b\u518d\u7248\u3002<\/li><\/ul><ul><li> <a class=\"external text\" href=\"http:\/\/www.cecm.sfu.ca\/~pborwein\/PAPERS\/P123.ps\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/www.cecm.sfu.ca\/~pborwein\/PAPERS\/P123.ps\">\u30d9\u30a4\u30ea\u30fc\u3001D.\u30dc\u30fc\u30ef\u30a4\u30f3\u3001P.\u304a\u3088\u3073 Plouffe, S.\u300c\u3055\u307e\u3056\u307e\u306a\u591a\u5bfe\u6570\u5b9a\u6570\u306e\u9ad8\u901f\u8a08\u7b97\u306b\u3064\u3044\u3066\u300d\u3002<\/a><\/li><\/ul><ul><li> <a class=\"external text\" href=\"http:\/\/xxx.lanl.gov\/abs\/math.CA\/9906134\/\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/xxx.lanl.gov\/abs\/math.CA\/9906134\/\">\u30d9\u30a4\u30ea\u30fc\u3001DH \u3068\u30d6\u30ed\u30fc\u30c9\u30cf\u30fc\u30b9\u30c8\u3001DJ\u300c17 \u6b21\u591a\u5bfe\u6570\u30e9\u30c0\u30fc\u300d\u3002 1999\u5e746\u670820\u65e5\u3002<\/a><\/li><\/ul><ul><li> Boersma, J. \u304a\u3088\u3073 Dempsey, JP\u300c\u30eb\u30b8\u30e3\u30f3\u30c9\u30eb\u306e\u30ab\u30a4\u95a2\u6570\u306e\u8a55\u4fa1\u306b\u3064\u3044\u3066\u300d\u3001Mathematics of Computation\u300159\u3001199\u3001pp. 157-163\u30011992\u5e74\u3002<\/li><\/ul><ul><li>\u30dc\u30fc\u30a6\u30a3\u30f3\u3001JM\u3002\u30d6\u30e9\u30c3\u30c9\u30ea\u30fc\u3001DM\u3002\u30d6\u30ed\u30fc\u30c9\u30cf\u30fc\u30b9\u30c8\u3001DJ\u3002\u304a\u3088\u3073Lisonek\u3001P.\u300c\u591a\u6b21\u5143\u591a\u5bfe\u6570\u306e\u7279\u5225\u306a\u5024\u300d\u3002 CECM-98:106\u30015 \u6708 14 \u65e5\u3002 <a class=\"external free\" href=\"http:\/\/www.cecm.sfu.ca\/preprints\/1998pp.html\\#98:106\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/www.cecm.sfu.ca\/preprints\/1998pp.html\\#98:106\">http:\/\/www.cecm.sfu.ca\/preprints\/1998pp.html\\#98:106<\/a><\/li><\/ul><ul><li> <a class=\"external text\" href=\"http:\/\/xxx.lanl.gov\/abs\/math.CA\/9910045\/\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/xxx.lanl.gov\/abs\/math.CA\/9910045\/\">\u30dc\u30fc\u30a6\u30a3\u30f3\u3001JM\u3002\u30d6\u30e9\u30c3\u30c9\u30ea\u30fc\u3001DM\u3002\u30d6\u30ed\u30fc\u30c9\u30cf\u30fc\u30b9\u30c8\u3001DJ\u3002\u304a\u3088\u3073Lisonek\u3001P.\u300c\u591a\u6b21\u5143\u591a\u5bfe\u6570\u306e\u7279\u5225\u306a\u5024\u300d\u3002 1999 \u5e74 10 \u6708 8 \u65e5\u3002<\/a><\/li><\/ul><ul><li>\u30d9\u30eb\u30f3\u30c8\u3001BC \u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306e\u30ce\u30fc\u30c8\u3001\u30d1\u30fc\u30c8 IV\u3002<span><a href=\"https:\/\/science-hub.click\/?p=22164\">\u30cb\u30e5\u30fc\u30e8\u30fc\u30af<\/a><\/span>: Springer-Verlag\u3001pp. 323-326\u30011994\u5e74\u3002<\/li><\/ul><ul><li> Clunie, J.\u3001\u300c\u30dc\u30fc\u30ba \u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u95a2\u6570\u306b\u3064\u3044\u3066\u300d\u3001\u7269\u7406\u5b66\u4f1a\u8ad6\u6587\u96c6\u3001\u30bb\u30af\u30b7\u30e7\u30f3 A\u300167\u3001pp. 632-636\u30011954 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title=\"http:\/\/www.gnu.org\/software\/gsl\/manual\/gsl-ref.html#SEC117\">GNU Scientific Library &#8211; \u30ea\u30d5\u30a1\u30ec\u30f3\u30b9 \u30de\u30cb\u30e5\u30a2\u30eb<\/a>cf GNU Scientific Library<\/li><\/ul><ul><li> Jahnke, E. \u304a\u3088\u3073 Emde, F.\u3001\u5f0f\u3068\u66f2\u7dda\u3092\u542b\u3080\u95a2\u6570\u8868\u3001\u30c9\u30fc\u30d0\u30fc\u30011945 \u5e74\u3002<\/li><\/ul><ul><li> K\u00f6lbig, KS\u3001Mignaco, JA\u3001\u304a\u3088\u3073 Remiddi, E.\u3001\u300c\u30cb\u30fc\u30eb\u30bb\u30f3\u306e\u4e00\u822c\u5316\u591a\u5bfe\u6570\u3068\u305d\u306e\u6570\u5024\u8a08\u7b97\u306b\u3064\u3044\u3066\u300d\u3001 <span><a href=\"https:\/\/science-hub.click\/?p=50969\">BIT<\/a><\/span> \u300110\u3001pp. 38-74\u30011970\u5e74\u3002<\/li><\/ul><ul><li> K\u00f6lbig\u3001KS\u300c\u30cb\u30fc\u30eb\u30bb\u30f3\u306e\u4e00\u822c\u5316\u591a\u5bfe\u6570\u300d\u3001SIAM J. 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A.\u300c\u4e00\u822c\u5316\u30bc\u30fc\u30bf\u95a2\u6570\u3001\u30d9\u30eb\u30cc\u30fc\u30a4\u591a\u9805\u5f0f\u3001\u30aa\u30a4\u30e9\u30fc\u591a\u9805\u5f0f\u3001\u304a\u3088\u3073\u591a\u91cd\u5bfe\u6570\u300d\u3002\u7a4d\u5206\u3068\u7d1a\u6570\u3001Vol. 1.2 \u3092\u53c2\u7167\u3002 3: \u3088\u308a\u7279\u5225\u306a\u6a5f\u80fd\u3002\u30cb\u30e5\u30fc\u30b8\u30e3\u30fc\u30b8\u30fc\u5dde\u30cb\u30e5\u30fc\u30a2\u30fc\u30af: \u30b4\u30fc\u30c9\u30f3\u3068\u30d6\u30ea\u30fc\u30c1\u3001p. 1990 \u5e74 23 \uff5e 24 \u65e5\u3002<\/li><\/ul><ul><li> <a class=\"external text\" href=\"http:\/\/prola.aps.org\/abstract\/PR\/v83\/i3\/p678_1\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/prola.aps.org\/abstract\/PR\/v83\/i3\/p678_1\">Robinson, JE\u300c\u30dc\u30fc\u30ba\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u7a4d\u5206\u95a2\u6570\u306b\u95a2\u3059\u308b\u6ce8\u8a18\u300d\u3001Physical Review\u3001\u30b7\u30ea\u30fc\u30ba 2\u300183\u3001pp. 678-679\u30011951\u5e74\u3002<\/a><\/li><\/ul><ul><li> Schr\u00f6dinger, E.\u3001\u7d71\u8a08\u71b1\u529b\u5b66\u3001\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u30011952 \u5e74\u3002<\/li><\/ul><ul><li> Truesdell, C.\u300c\u30dd\u30ea\u30de\u30fc\u306e\u69cb\u9020\u7406\u8ad6\u3067\u767a\u751f\u3059\u308b<span>\u95a2\u6570<\/span>\u306b\u3064\u3044\u3066\u300d\u3001Annals of Mathematics\u3001\u30b7\u30ea\u30fc\u30ba 2\u300146\u3001No 1\u3001pp. 144 \uff5e 1457 \u5e74\u30011945 \u5e74\u3002<\/li><\/ul><ul><li> Whittaker, ET\u3001Watson, GN\u3001\u300e\u73fe\u4ee3\u5206\u6790<span>\u30b3\u30fc\u30b9<\/span>\u300f\u3001\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u30011927 \u5e74\u3002<\/li><\/ul><ul><li> <a class=\"external text\" href=\"http:\/\/www.cs.kent.ac.uk\/pubs\/1992\/110\/\" rel=\"nofollow\" target=\"blank\" title=\"http:\/\/www.cs.kent.ac.uk\/pubs\/1992\/110\/\">Wood\u3001David C.\u3001\u6280\u8853\u30ec\u30dd\u30fc\u30c8 15-92\u3001\u30b1\u30f3\u30c8\u5927\u5b66\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u7814\u7a76\u6240\u3001<\/a>\u30b1\u30f3\u30c8\u5927\u5b66\u3001\u30ab\u30f3\u30bf\u30d9\u30ea\u30fc\u3001\u82f1\u56fd\u30011992 \u5e74 6 \u6708\u3002<\/li><\/ul><ul><li> Zagier, D.\u300c\u591a\u91cd\u5bfe\u6570\u306e\u7279\u6b8a\u306a\u5024\u3068\u95a2\u6570\u65b9\u7a0b\u5f0f\u300d\u3002 \u300e\u591a\u5bfe\u6570\u306e\u69cb\u9020\u7279\u6027\u300f\u306e\u4ed8\u9332 A (L. Lewin \u7de8)\u3002\u30ed\u30fc\u30c9\u30a2\u30a4\u30e9\u30f3\u30c9\u5dde\u30d7\u30ed\u30d3\u30c7\u30f3\u30b9: \u82e6\u3044\u3067\u3059\u3002\u6570\u5b66\u3002\u5b66\u4f1a\u30011991 \u5e74\u3002<\/li><\/ul><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%AA%D8%B9%D8%AF%D8%AF_%D8%A7%D9%84%D9%84%D9%88%D8%BA%D8%A7%D8%B1%D9%8A%D8%AA%D9%85%D8%A7%D8%AA\">\u0645\u062a\u0639\u062f\u062f \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u0627\u062a \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/bg.wikipedia.org\/wiki\/%D0%9F%D0%BE%D0%BB%D0%B8%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D1%8A%D0%BC\">\u041f\u043e\u043b\u0438\u043b\u043e\u0433\u0430\u0440\u0438\u0442\u044a\u043c \u2013 bulgare<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Polylogarithmus\">Polylogarithmus \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Polylogarithm\">Polylogarithm \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Funci%C3%B3n_polilogar%C3%ADtmica\">Funci\u00f3n polilogar\u00edtmica \u2013 espagnol<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/fa.wikipedia.org\/wiki\/%D9%BE%D9%84%DB%8C%E2%80%8C%D9%84%DA%AF%D8%A7%D8%B1%DB%8C%D8%AA%D9%85\">\u067e\u0644\u06cc\u200c\u0644\u06af\u0627\u0631\u06cc\u062a\u0645 \u2013 persan<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u3010\u5171\u901a\u30c6\u30b9\u30c8\u5bfe\u7b56\u3011log\u306e\u88cf\u30ef\u30b6\u3092\u4f7f\u3063\u3066\u77ac\u6bba\u305b\u3088\uff01\uff01\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ffXqn2ZmrIY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u591a\u5bfe\u6570\u95a2\u6570(\u30b8\u30e7\u30f3\u30ad\u30a8\u30fc\u30eb\u95a2\u6570\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u307e\u3059) \u306f\u6ce8\u76ee\u306b\u5024\u3059\u308b\u95a2\u6570\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306es\u304a\u3088\u3073 |z|&lt;1 \u306b\u5bfe\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 $$ {Li_s(z) \\equiv \\sum_{k=1}^\\inf [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32105,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/nbipBrmV0iI\/0.jpg","fifu_image_alt":"\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[11,13,14,10,12,33017,33016,16,15,1839],"class_list":["post-32104","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-dossier","tag-polylogarithme","tag-fonction-polylogarithme","tag-sciences","tag-article","tag-fonction"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/32104"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32104"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/32104\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/32105"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}