[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/260#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/260","headline":"\u6a5f\u80fd\u03b3-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u6a5f\u80fd\u03b3-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 2017-03\u306e\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u63d0\u4f9b\u3055\u308c\u305f\u60c5\u5831\u306e\u691c\u8a3c\u304c\u5fc5\u8981\u3067\u3059\u3002 \u4fe1\u983c\u3067\u304d\u308b\u60c5\u5831\u6e90\u306f\u3001\u597d\u307e\u3057\u304f\u306f\u66f8\u8a8c\u7684\u306a\u811a\u6ce8\u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u3079\u304d\u3067\u3059\u3002 \u8a18\u4e8b\u306e\u4e00\u90e8\u307e\u305f\u306f\u3059\u3079\u3066\u306e\u60c5\u5831\u3067\u3055\u3048\u3001\u771f\u5b9f\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30bd\u30fc\u30b9\u3092\u6b20\u3044\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u305d\u308c\u3089\u306f\u6311\u6226\u3057\u3066\u524a\u9664\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002 \u3053\u306e\u8a18\u4e8b\u306e\u8b70\u8ad6\u306b\u306f\u3001\u4f55\u3092\u4fee\u6b63\u3059\u3079\u304d\u304b\u306b\u3064\u3044\u3066\u306e\u3088\u308a\u8a73\u7d30\u306a\u60c5\u5831\u304c\u3042\u308a\u307e\u3059\u3002 \u6b20\u9665\u3092\u6392\u9664\u3057\u305f\u5f8c\u3001\u3053\u306e\u8a18\u4e8b\u304b\u3089\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8{{refine}}\u3092\u524a\u9664\u3057\u307e\u3059\u3002 \u30ac\u30f3\u30de\u95a2\u6570 \uff08\u30a8\u30a6\u30eb\u30e9\u30ac\u30f3\u30de\u3068\u3082\u547c\u3070\u308c\u307e\u3059\uff09 &#8211; \u5f37\u3044\u6982\u5ff5\u3092\u62e1\u5f35\u3059\u308b\u7279\u5225\u306a\u6a5f\u80fd [\u521d\u3081] \u5b9f\u969b\u306e\u6570\u5b57\u3068\u8907\u96d1\u306a\u6570\u5b57\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3002\u8907\u96d1\u306a\u6570\u306e\u5b9f\u969b\u306e\u90e8\u5206 \u3068 \u305d\u308c\u306f\u30dd\u30b8\u30c6\u30a3\u30d6\u3067\u3042\u308a\u3001\u305d\u308c\u306f\u5b8c\u5168\u3067\u3059\uff08\u30aa\u30a4\u30ec\u30e9\u306e\u7a4d\u5206\uff09\uff1a c \uff08 \u3068 \uff09\uff09 = \u222b0+\u221etz\u22121e\u2212td","datePublished":"2023-07-19","dateModified":"2023-07-19","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/260","wordCount":7831,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x42017-03\u306e\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u63d0\u4f9b\u3055\u308c\u305f\u60c5\u5831\u306e\u691c\u8a3c\u304c\u5fc5\u8981\u3067\u3059\u3002 \u4fe1\u983c\u3067\u304d\u308b\u60c5\u5831\u6e90\u306f\u3001\u597d\u307e\u3057\u304f\u306f\u66f8\u8a8c\u7684\u306a\u811a\u6ce8\u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u3079\u304d\u3067\u3059\u3002 \u8a18\u4e8b\u306e\u4e00\u90e8\u307e\u305f\u306f\u3059\u3079\u3066\u306e\u60c5\u5831\u3067\u3055\u3048\u3001\u771f\u5b9f\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30bd\u30fc\u30b9\u3092\u6b20\u3044\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u305d\u308c\u3089\u306f\u6311\u6226\u3057\u3066\u524a\u9664\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002 \u3053\u306e\u8a18\u4e8b\u306e\u8b70\u8ad6\u306b\u306f\u3001\u4f55\u3092\u4fee\u6b63\u3059\u3079\u304d\u304b\u306b\u3064\u3044\u3066\u306e\u3088\u308a\u8a73\u7d30\u306a\u60c5\u5831\u304c\u3042\u308a\u307e\u3059\u3002 \u6b20\u9665\u3092\u6392\u9664\u3057\u305f\u5f8c\u3001\u3053\u306e\u8a18\u4e8b\u304b\u3089\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8{{refine}}\u3092\u524a\u9664\u3057\u307e\u3059\u3002  \u30ac\u30f3\u30de\u95a2\u6570 \uff08\u30a8\u30a6\u30eb\u30e9\u30ac\u30f3\u30de\u3068\u3082\u547c\u3070\u308c\u307e\u3059\uff09 &#8211; \u5f37\u3044\u6982\u5ff5\u3092\u62e1\u5f35\u3059\u308b\u7279\u5225\u306a\u6a5f\u80fd [\u521d\u3081] \u5b9f\u969b\u306e\u6570\u5b57\u3068\u8907\u96d1\u306a\u6570\u5b57\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3002\u8907\u96d1\u306a\u6570\u306e\u5b9f\u969b\u306e\u90e8\u5206 \u3068 \u305d\u308c\u306f\u30dd\u30b8\u30c6\u30a3\u30d6\u3067\u3042\u308a\u3001\u305d\u308c\u306f\u5b8c\u5168\u3067\u3059\uff08\u30aa\u30a4\u30ec\u30e9\u306e\u7a4d\u5206\uff09\uff1a c \uff08 \u3068 \uff09\uff09 = \u222b0+\u221etz\u22121e\u2212td t {displaystyle\u30ac\u30f3\u30de\uff08z\uff09= int limits _ {0}^{+infty} t^{z-1}\u3001e^{ &#8211;  t}\u3001dt} \u305d\u308c\u306f\u5bb9\u8d66\u306a\u304f\u53ce\u675f\u3057\u3066\u3044\u307e\u3059\u3002\u90e8\u54c1\u3092\u4ecb\u3057\u3066\u7d71\u5408\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6b21\u306e\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 c \uff08 \u3068 + \u521d\u3081 \uff09\uff09 = \u3068 de c \uff08 \u3068 \uff09\uff09 \u3002 {displaystyle\u30ac\u30f3\u30de\uff08z+1\uff09= zcdot\u30ac\u30f3\u30de\uff08z\uff09\u3002} \u03b3\uff081\uff09= 1\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u4e0a\u8a18\u306e\u30d1\u30bf\u30fc\u30f3\u306f\u03b3\uff08 n +1\uff09= n \uff01\u3059\u3079\u3066\u306e\u81ea\u7136\u6570\u306e\u305f\u3081\u306b n \u3002 \u03b3\u95a2\u6570\u3092\u6c7a\u5b9a\u3059\u308b2\u756a\u76ee\u306e\u65b9\u6cd5\uff08\u4efb\u610f\u306e\u8907\u96d1\u306a\u6570\u5b57\uff09\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 c \uff08 \u3068 \uff09\uff09 = limn\u2192+\u221en!nzz(z+1)(z+2)\u2026(z+n)= 1z\u220fn=1\u221e(1+1n)z1+zn\u3002 {displaystyle gamma\uff08z\uff09= lim _ {nrightarrow+infty} {frac {n\uff01n^{z}} {z\uff08z+1\uff09\uff08z+2\uff09ldots\uff08z+n\uff09}} = {frac {1} {z}}} {frac {n} {z} {z}}}}}}}}} {Z}} {Z} {Z} {Z} {Z} {Z}}}}} {z} {n}}}}}}\u3002} \u307e\u305f\u3001\u30ac\u30f3\u30de\u95a2\u6570\u306e\u53cd\u5bfe\u3092\u6b21\u306e\u3088\u3046\u306b\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\uff08\u03b3\u306fEulera-Mascheroni\u306e\u5b9a\u6570\u3067\u3059\uff09\uff1a 1\u0393(z)= \u3068 e\u03b3z\u220fn=1\u221e[(1+zn)e\u2212zn]\u3002 {displaystyle {frac {1} {gamma\uff08z\uff09}}} = ze^{gamma z} prod _ {n = 1}^{infty}\u5de6[1+ {frac {z} {n}}\u53f3\uff09e^{ &#8211;  {z} {n}}}}}} \u30ac\u30f3\u30de\u95a2\u6570\u306b\u306f\u30bc\u30ed\u306e\u5834\u6240\u304c\u3042\u308a\u307e\u305b\u3093\u3002 \u305d\u308c\u306f\u5b8c\u5168\u306a\u30dd\u30a4\u30f3\u30c8\u3067\u4e0d\u9023\u7d9a\u3067\u3042\u308a\u3001\u5de6\u53f3\u306e\u3053\u308c\u3089\u306e\u5730\u70b9\u3067\u5de6\u53f3\u306b\u63a1\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002 [\u5fc5\u8981] \u3002 c \uff08 \u3068 + \u521d\u3081 \uff09\uff09 = \u3068 de c \uff08 \u3068 \uff09\uff09 {displaystyle\u30ac\u30f3\u30de\uff08z+1\uff09= zcdot\u30ac\u30f3\u30de\uff08z\uff09} c \uff08 \u3068 \uff09\uff09 de c (z+12)= \u03c022\u22c5z\u00a0\u22121de c \uff08 2 \u3068 \uff09\uff09 {displaystyle\u30ac\u30f3\u30de\uff08z\uff09CDOT\u30ac\u30f3\u30de\u5de6\uff08z+{frac {1} {2}}\u53f3\uff09= {frac {sqrt {pi}} {2^{2cdot z -1}}} cdot\u30ac\u30f3\u30de\uff082z\uff09}} \u5206\u6bcd\u304c\u30bc\u30ed\u3067\u306a\u3044\u5834\u5408\u3001\u6b21\u306e2\u3064\u306e\u8a2d\u8a08\u304c\u767a\u751f\u3057\u307e\u3059\u3002 c \uff08 \u3068 \uff09\uff09 de c \uff08 \u521d\u3081  &#8211;  \u3068 \uff09\uff09 = \u03c0sin\u2061\u03c0z\u3001 {displaystyle\u30ac\u30f3\u30de\uff08z\uff09cdot\u30ac\u30f3\u30de\uff081-z\uff09= {frac {pi} {sin {pi z}}}\u3001} c (z+12)de c (12\u2212z)= \u03c0cos\u2061\u03c0z\u3002 {displaystyle gamma\u5de6\uff08z+{frac {1} {2}}\u53f3\uff09cdot\u30ac\u30f3\u30de\u5de6\uff08{frac {1} {2} {2}}  &#8211;  zright\uff09= {frac {pi} {cos {pi z}}}\u3002}}} \u3082\u3057\u3082  &#8211;  \u521d\u3081 < \u518d \u2061 \uff08 \u3068 \uff09\uff09 < \u521d\u3081 \u3001 {displaystyle -1 \u03c02z\u222b0\u221etz\u22121\u7f6a \u2061 td t \u3002 {displaystyle gamma\uff08z\uff09= {frac {1} {sin {{frac {pi} {2} z}}}} int _ {0}^{infty} t^{z-1} sin {t} dt\u3002}} \u3082\u3057\u3082 0 < \u518d \u2061 \uff08 \u3068 \uff09\uff09 < \u521d\u3081 \u3001 {displaystyle 0 \u03c02z\u222b0\u221etz\u22121cos \u2061 td t \u3002 {displaystyle gamma\uff08z\uff09= {frac {1} {cos {frac {pi} {2} z}}} int _ {0}^{infty} t^{z-1} cos {t} dt\u3002}} \u30ac\u30a6\u30b9\u306e\u88fd\u54c1\u30d1\u30bf\u30fc\u30f3\uff1a c \uff08 n \u3068 \uff09\uff09 = nnz(2\u03c0)n\u22121de c \uff08 \u3068 \uff09\uff09 de c (z+1n)de c (z+2n)de &#8230; de c (z+n\u22121n)\u3002 {displaystyle gamma\uff08nz\uff09= {frac {n^{nz}} {sqrt {\uff082pi\uff09^{n-1}}}} cdot\u30ac\u30f3\u30de\u5de6\uff08z+{frac {1} {n}}\u53f3\u53f3\u53f3nd {nz {n}} cdot\u30ac\u30f3\u30de\u5de6\uff08z+{frac {2 frac {frac {frac {frac\uff09{frac {frac {frac {frac\uff09\u5de6\uff08z+{frac {n-1} {n}}\u53f3\uff09\u3002} \u305f\u3081\u306b n \u5408\u8a08\u3001\u30dd\u30b8\u30c6\u30a3\u30d6\uff1a c \uff08 n \uff09\uff09  =  \uff08 n  &#8211;  \u521d\u3081 \uff09\uff09 \uff01 \u3001 {displaystyle\u30ac\u30f3\u30de\uff08n\uff09=\uff08n-1\uff09\uff01} c (n+12)= (2n\u22121)!!2n\u03c0\u3001 {displaystyle\u30ac\u30f3\u30de\u5de6\uff08n+{frac {1} {2}}\u53f3\uff09= {frac {\uff082n-1\uff09!!} {2^{n}}} {sqrt {pi}}\u3001} c \uff08 n + \u521d\u3081 \/p \uff09\uff09 = c \uff08 \u521d\u3081 \/p \uff09\uff09 (pn\u2212(p\u22121))!(p)pn\u3001 {displaystyle\u30ac\u30f3\u30de\uff08n+1\/p\uff09=\u30ac\u30f3\u30de\uff081\/p\uff09{frac {\uff08pn-\uff08p-1\uff09\uff09\uff01^{\uff08p\uff09}} {p^{n}}}\u3001} \u3069\u3053 \u30d0\u30c4 \uff01 (p){displaystyle x\uff01^{\uff08p\uff09}} \u610f\u5473\u304c\u3042\u308a\u307e\u3059\u8907\u6570\u306ep-\u3053\u308c\u306f\u5f37\u3044\u3002 Table of Contents\u30d5\u30a3\u30fc\u30eb\u30c9\u30ab\u30e9\u30fc\u30ea\u30f3\u30b0\u6280\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5f15\u6570\u3067\u8272\u4ed8\u3051\u3055\u308c\u305f\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u7a7a\u9593\u6295\u5f71 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ac\u30f3\u30de\u95a2\u6570\u306e\u9078\u629e\u3055\u308c\u305f\u5024 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ac\u30f3\u30de\u95a2\u6570\u306e\u5bfe\u6570\u5fae\u5206 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d5\u30a3\u30fc\u30eb\u30c9\u30ab\u30e9\u30fc\u30ea\u30f3\u30b0\u6280\u8853 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5b8c\u5168\u306a\u30c1\u30e3\u30fc\u30c8        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30e2\u30b8\u30e5\u30fc\u30eb \u53e3\u8ad6 \u672c\u5f53\u306e\u90e8\u5206 \u60f3\u50cf\u4e0a\u306e\u4e00\u90e8        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5f15\u6570\u3067\u8272\u4ed8\u3051\u3055\u308c\u305f\u30e2\u30b8\u30e5\u30fc\u30eb\u306e\u7a7a\u9593\u6295\u5f71 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u8ef8 \u30d0\u30c4  &#8211; \u5b9f\u969b\u306e\u90e8\u5206\u3001\u8ef8 \u3068  &#8211; \u8eca\u8ef8 &#8211; \u5f62\u306e\u90e8\u5206\u3001\u8ef8 \u3068  &#8211; \u7d50\u679c\u30e2\u30b8\u30e5\u30fc\u30eb\u3001 \u8272  &#8211; \u7d50\u679c\u306e\u5f15\u6570 \u30ac\u30f3\u30de\u95a2\u6570\u306e\u9078\u629e\u3055\u308c\u305f\u5024 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u0393(\u22122)\u2212\u0393(\u22123\/2)=4\u03c03\u22482,363271801\u0393(\u22121)\u2212\u0393(\u22121\/2)=\u22122\u03c0\u2248\u22123,544907702\u0393(0)\u2212\u0393(1\/7)\u22486,548062940\u0393(1\/6)\u22485,566316002\u0393(1\/5)\u22484,590843712\u0393(1\/4)\u22483,625609908\u0393(1\/3)\u22482,678938535\u0393(1\/2)=\u03c0\u22481,772453851\u0393(1)=0!=1\u0393(xmin)=0,885603194\u0393(3\/2)=\u03c02\u22480,886226925\u0393(2)=1!=1\u0393(5\/2)=3\u03c04\u22481,329340388\u0393(3)=2!=2\u0393(7\/2)=15\u03c08\u22483,323350970\u0393(4)=3!=6{displayStyle {begin {array} {lll} gamma\uff08-2\uff09\uff06 &#8211; \uff06\\ gamma\uff08-3\/2\uff09\uff06= {frac {4 {sqrt {pi}}}}\uff06comprx 2 {\u3001} 363271801 \\ gamma\uff08}\uff06\\ gamma\uff08-1\uff09\uff06\\ f.-1\/2\uff09 i}}\uff06compx -3 {\u3001} 544907702 \\ gamma\uff080\uff09\uff06 &#8211; \uff06\\ gamma\uff081\/7\uff09&#038;&#038; artix 6 {\u3001} 548062940 \\ gamma\uff081\/6\uff09&#038;&#038; &#038;&#038; 5 {\u3001} 566316002 \/4\uff09&#038;&#038; amptx 3 {\u3001} 625609908 \\ gamma\uff081\/3\uff09&#038;&#038; rule somma\uff081\/2\uff09\uff06= {sqrt {pi}}\uff06cortx 1 {\u3001} 772453851 \\ gamma\uff081\uff09\\ gamma\uff081\uff09 0 {\u3001} 885603194 \\ gamma\uff083\/2\uff09\uff06= {frac {sqrt {pi}} {2}}\uff06compx 0 {\u3001} 886226925 \\ gamma\uff082\uff09\uff06= 1\uff01\uff06= 1 \\ gamma\uff085\/2\uff09\uff06= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = }\uff06compx 1 {\u3001} 329340388 \\ gamma\uff083\uff09\uff06= 2\uff01\uff06= 2 \\ gamma\uff087\/2\uff09\uff06= {frac {15 {sqrt {pi}} {8}}\uff06cortx 3 {\u3001} 323350970 \\ gamma\uff084\uff093\uff01 \u30d0\u30c4 min{displaystyle x_ {min}} \u3053\u308c\u306f\u03b3\u95a2\u6570\u306e\u305d\u306e\u3088\u3046\u306a\u8b70\u8ad6\u3067\u3042\u308a\u3001\u5c40\u6240\u7684\u306a\u6700\u5c0f\u5024\u3092\u63a1\u7528\u3057\u307e\u3059 \u30d0\u30c4 > 0\u3001        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30c4 min\u2248 1.461 632145\u3002 {displayStyle X_ {min}\u7d041 {\u3001} 461632145\u3002}  \u95a2\u6570\u03b3\uff08 \u3068 \uff09\u306b\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u305b\u3093 \u3068 0\u3001-1\u3001-2\u3001&#8230;\uff08ma boeguny oh restuum \uff08  &#8211;  \u521d\u3081 \uff09\uff09 n\/ n \uff01 {displaystyle\uff08-1\uff09^{n}\/n\uff01} \uff09\u3002 \u30ac\u30f3\u30de\u95a2\u6570\u306e\u5bfe\u6570\u5fae\u5206 [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u30ac\u30f3\u30de\u8a98\u5c0e\u4f53\u306e\u5bfe\u6570\u30c1\u30e3\u30fc\u30c8 \u95a2\u6570\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059 \u03c6 \uff08 \u3068 \uff09\uff09 \u3001 {displaystyle psi\uff08z\uff09\u3001} \u79c1\u305f\u3061\u304c\u547c\u3093\u3067\u3044\u307e\u3059 \u30ac\u30f3\u30de\u95a2\u6570\u306e\u5bfe\u6570\u5fae\u5206 \u307e\u305f digamma\u95a2\u6570 \uff1a \u03c6 \uff08 \u3068 \uff09\uff09 = \u0393\u2032(z)\u0393(z)\u3001 {displaystyle psi\uff08z\uff09= {frac {gamma &#8216;\uff08z\uff09} {gamma\uff08z\uff09}}\u3001} \u3069\u3053 \u3068 \u2260 0 \u3001  &#8211;  \u521d\u3081 \u3001  &#8211;  2 \u3001 &#8230; {displaystyle zneq 0\u3001-1\u3001-2\u3001dots} \u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\uff08 c {displaystyle\u30ac\u30f3\u30de} -Eulera-Mascheroni\u3092staw\u3057\u307e\u3057\u305f\uff09\uff1a \u03c6 \uff08 \u3068 \uff09\uff09 =  &#8211;  c + \u2211n=0\u221e(1n+1\u22121n+z)\u3001 {displaystyle psi\uff08z\uff09= -mamma+sum _ {n = 0}^{infty}\u5de6\uff08{frac {1} {n+1}}  &#8211;  {frac {1} {n+z}}\u53f3\uff09\u3001} \u03c8\u2032\uff08 \u3068 \uff09\uff09 = \u2211k=0\u221e1(z+k)2\u3002 {displaystyle psi &#8216;\uff08z\uff09= sum _ {k = 0}^{infty} {frac {1} {left\uff08z+kright\uff09^{2}}}\u3002}}} \u3055\u3089\u306b\u3001\u5927\u304d\u306a\u3082\u306e\u306e\u5834\u5408 \u30d0\u30c4 \u8fd1\u4f3c\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \u03c6 \uff08 \u30d0\u30c4 \uff09\uff09 \u2248 ln \u2061 \u30d0\u30c4  &#8211;  12x\u3002 {displaystyle psi\uff08x\uff09art rn x- {frac {1} {2x}}\u3002}}} \u95a2\u6570\u3082\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u03c8(n)\uff08 \u3068 \uff09\uff09 = dn\u03c8(z)dzn= (ddz)n+1ln \u2061 c \uff08 \u3068 \uff09\uff09 \u3001 {dissispastyle psi^{\uff08n\uff09}\uff08z\uff09= {frac {d^{n} psi\uff08z\uff09} {dz^{n}}}}}}}}}}}}}}}}}^{n+1} ln\u30ac\u30f3\u30de\uff08Z\uff09\u3001}} \u79c1\u305f\u3061\u304c\u547c\u3093\u3067\u3044\u307e\u3059 \u30dd\u30ea\u30ac\u30f3\u30de\u95a2\u6570 n -y\u6ce8\u6587 \u3002\u6b21\u306b\u3001Digamma\u95a2\u6570\u306f\u6b21\u200b\u200b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 \u03c6 \uff08 \u3068 \uff09\uff09 = \u03c8(0)\uff08 \u3068 \uff09\uff09 \u3002 {distrastaStyle psi\uff08z\uff09= psi ^{\uff080\uff09}\uff08z\uff09\u3002} \u6a5f\u80fd \u03c6 (1){displaystyle psi ^{\uff081\uff09}} Trigamma\u307e\u305f\u306fTri -Hall\u95a2\u6570\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002 Piebhammer\u306e\u30b7\u30f3\u30dc\u30eb\u306f\u30ac\u30f3\u30de\u95a2\u6570\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059 [2] \u3002 N\u6b21\u5143\u306e\u9ad8\u6b21\u5143\u4f53\u7a4d\u306e\u30d1\u30bf\u30fc\u30f3\uff1a Sn= \uff08 2 \u2217 \u03c0n\/2\uff09\uff09 \/\uff08 c \uff08 \u521d\u3081 \/2 n \uff09\uff09 \uff09\uff09 {displaystyle s_ {n} =\uff082*pi ^{n\/2}\uff09\/\uff08gamma\uff081\/2n\uff09\uff09} [3] \u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/260#breadcrumbitem","name":"\u6a5f\u80fd\u03b3-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]