[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/15703#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/15703","headline":"\u7d71\u5408\u57fa\u6e96-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","name":"\u7d71\u5408\u57fa\u6e96-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u7a4d\u5206\u57fa\u6e96 \uff08\u305d\u308c\u3082 Maclaurin-Cauchy Integral Starion [\u521d\u3081] \uff09 &#8211; \u7279\u5b9a\u306e\u884c\u3092\u7a4d\u5206\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3044\u3046\u8003\u3048\u306b\u57fa\u3065\u3044\u3066\u3001\u30e9\u30f3\u30af\u306e\u53ce\u675f\u306e\u80af\u5b9a\u7684\u306a\u5358\u8a9e\u3068\u306e\u53ce\u675f\u306e\u57fa\u6e96\u3002\u3053\u306e\u57fa\u6e96\u306e\u521d\u671f\u306e\u5f62\u5f0f\u306f\u3001\u30a4\u30f3\u30c9\u3067\u30de\u30c0\u30ef\u306b\u3088\u3063\u3066\u767a\u898b\u3055\u308c\u307e\u3057\u305f [2] 14\u4e16\u7d00\u3068\u30b1\u30e9\u30e9\u5dde\u306e\u5b66\u6821\u306e\u5f8c\u7d99\u8005\u3002\u30e8\u30fc\u30ed\u30c3\u30d1\u3067\u306f\u30011742\u5e74\u306b\u30de\u30af\u30e9\u30a6\u30ea\u30f3\u306b\u3088\u3063\u3066\u518d\u3073\u57fa\u6e96\u304c\u518d\u3073\u767a\u898b\u3055\u308c\u307e\u3057\u305f [3] \u79c1\u306fcauchy\u2019ego\u3067\u3059 [4] \u3002 after-content-x4 \u3055\u305b\u3066 f \uff1a","datePublished":"2019-04-26","dateModified":"2019-04-26","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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/fa1e605f8b04ee3a521f791e24407b61269c1856","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/fa1e605f8b04ee3a521f791e24407b61269c1856","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/15703","wordCount":6228,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u7a4d\u5206\u57fa\u6e96 \uff08\u305d\u308c\u3082 Maclaurin-Cauchy Integral Starion [\u521d\u3081] \uff09 &#8211; \u7279\u5b9a\u306e\u884c\u3092\u7a4d\u5206\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3044\u3046\u8003\u3048\u306b\u57fa\u3065\u3044\u3066\u3001\u30e9\u30f3\u30af\u306e\u53ce\u675f\u306e\u80af\u5b9a\u7684\u306a\u5358\u8a9e\u3068\u306e\u53ce\u675f\u306e\u57fa\u6e96\u3002\u3053\u306e\u57fa\u6e96\u306e\u521d\u671f\u306e\u5f62\u5f0f\u306f\u3001\u30a4\u30f3\u30c9\u3067\u30de\u30c0\u30ef\u306b\u3088\u3063\u3066\u767a\u898b\u3055\u308c\u307e\u3057\u305f [2] 14\u4e16\u7d00\u3068\u30b1\u30e9\u30e9\u5dde\u306e\u5b66\u6821\u306e\u5f8c\u7d99\u8005\u3002\u30e8\u30fc\u30ed\u30c3\u30d1\u3067\u306f\u30011742\u5e74\u306b\u30de\u30af\u30e9\u30a6\u30ea\u30f3\u306b\u3088\u3063\u3066\u518d\u3073\u57fa\u6e96\u304c\u518d\u3073\u767a\u898b\u3055\u308c\u307e\u3057\u305f [3] \u79c1\u306fcauchy\u2019ego\u3067\u3059 [4] \u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3055\u305b\u3066 f \uff1a [ \u521d\u3081 \u3001 \u221e \uff09\uff09 \u2192 r {displaystyle fcolon [1\u3001infty\uff09to mathbb {r}} \u305d\u308c\u306f\u6b63\u3067\u6e1b\u5c11\u3059\u308b\u6a5f\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3055\u305b\u3066 a n= f \uff08 n \uff09\uff09 {displaystyle a_ {n} = f\uff08n\uff09} \u3059\u3079\u3066\u306e\u4eba\u306e\u305f\u3081\u306b        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4n \u3002 {displaystyle n\u3002} \u305d\u306e\u5f8c\u3001\u30b7\u30ea\u30fc\u30ba \u2211n=1\u221ean{displaystyle sum _ {n = 1}^{infty} a_ {n}}}}  \uff08a\uff09 \u305d\u308c\u306f\u4e00\u81f4\u3057\u3001\u7a4d\u5206\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u306e\u307f [5]        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u222b1\u221ef(x)dx.{displaystyle int limits _ {1}^{infty} f\uff08x\uff09\u3001mathrm {d} x\u3002}  \uff08\u79c1\uff09  \u95a2\u6570\u306e\u30b0\u30e9\u30d5 y=2x{displaystyle y = {frac {2} {x}}} \u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u5185 [1,\u221e){displaystyle [1\u3001infty\uff09} \u7a4d\u5206\uff08i\uff09\u306f\u3001\u66f2\u7dda\u4e0b\u306e\u9818\u57df\u306e\u9762\u7a4d\u3092\u8868\u73fe\u3057\u307e\u3059 \u3068 = f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = f\uff08x\uff09} \uff08\u9ed2\u306e\u96a3\u306e\u56f3\uff09\u7bc4\u56f2\u5185 [ \u521d\u3081 \u3001 \u221e \uff09\uff09 \u3002 {displaystyle [1\u3001infty\uff09\u3002} \u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u30dd\u30a4\u30f3\u30c8\u306e\u30c1\u30e3\u30fc\u30c8\u306e\u30b5\u30a4\u30ba\u3092\u4e0e\u3048\u308b \u30d0\u30c4 = \u521d\u3081 \u3001 2 \u3001 &#8230; \u3001 {displaystyle x = 1,2\u3001dots\u3001} \u3060\u304b\u3089\u5f7c\u3089\u306f\u57fa\u3065\u3044\u3066\u9577\u65b9\u5f62\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u8868\u73fe\u3057\u307e\u3059 \u521d\u3081 {displaystyle1} \u305d\u3057\u3066\u9ad8\u3055 a n{displaystyle a_ {n}} \uff08\u305d\u306e\u96a3\u306e\u56f3\u3067\u306f\u3001\u7dd1\u3068\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059\uff09\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u306e\u5408\u8a08\u306f\u3001\u9577\u65b9\u5f62\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u5408\u8a08\u3067\u3059\u3002\u3053\u308c\u3092\u8003\u616e\u3057\u3066\u3001\u7a4d\u5206\u57fa\u6e96\u306f\u6b21\u306e\u3088\u3046\u306b\u89e3\u91c8\u3067\u304d\u307e\u3059\u3002\u30c1\u30e3\u30fc\u30c8\u306e\u4e0b\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u5834\u5408 \u3068 = f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = f\uff08x\uff09} \u305d\u308c\u306f\u7d42\u308f\u308a\u307e\u3057\u305f\u3001\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u5408\u8a08\u306f\u3055\u3089\u306b\u7d42\u308f\u308a\u307e\u3057\u305f \u521d\u3081 de a n{displaystyle 1cdot a_ {n}} \uff08\u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u306e\u5408\u8a08\u306b\u7b49\u3057\u3044\uff09\u3002 Fr.\u306e\u5404\u9577\u65b9\u5f62\u3092\u79fb\u52d5\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3002 \u521d\u3081 {displaystyle1} \u53f3\u5074\u306b\u3001\u30c1\u30e3\u30fc\u30c8 \u3068 = f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = f\uff08x\uff09} \u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u5185 [ 2 \u3001 \u221e \uff09\uff09 {displaystyle [2\u3001infty\uff09} \u524d\u8ff0\u306e\u30b7\u30d5\u30c8\u306e\u56f3\u306b\u542b\u307e\u308c\u307e\u3059\u3002\u7279\u306b\u3001\u30c1\u30e3\u30fc\u30c8\u306e\u4e0b\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u5834\u5408 \u3068 = f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = f\uff08x\uff09} \u305d\u308c\u306f\u7121\u9650\u3067\u3042\u308a\u3001\u307e\u305f\u3001\u8003\u616e\u3055\u308c\u305f\u56f3\u306e\u30d5\u30a3\u30fc\u30eb\u30c9\u306b\u3082\u7121\u9650\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u305a\u3001\u3057\u305f\u304c\u3063\u3066\u884c\u306e\u5408\u8a08\uff08a\uff09 [6] \u3002 \u95a2\u6570\u306e\u305f\u3081 f {displaystyle f} \u6e1b\u5c11\u3057\u3066\u304a\u308a\u3001\u4e0d\u5747\u4e00\u6027\u304c\u3042\u308a\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 \u2a7d ak{displaystyle f\uff08x\uff09leqslant a_ {k}} \u305f\u3081\u306b k \u2a7d \u30d0\u30c4 \u2a7d k + \u521d\u3081 \u3001 {displaystyle kleqslant xleqslant k+1\u3001} ak\u2a7d f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle a_ {k} leqslant f\uff08x\uff09} \u305f\u3081\u306b k  &#8211;  \u521d\u3081 \u2a7d \u30d0\u30c4 \u2a7d k \u3002 {displaystyle k-1leqslant xleqslant k\u3002} \u3053\u306e\u610f\u5473\u306f \u222bkk+1f \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2a7d ak\u2a7d \u222bk\u22121kf \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \uff08 k = 2 \u3001 3 &#8230; \uff09\uff09 \u3001 {displaystyle int limits _ {k}^{k+1} f\uff08x\uff09\u3001mathrm {d} xleqslant a_ {k} leqslant int limits _ {k-1}^{k} f\uff08x\uff09\u3001mathrm {d} xquad\uff08k\u3001= 2,3ldots\uff09\u3001} \u305d\u3057\u3066\u3053\u3053\u304b\u3089 a2+ &#8230; + an\u2a7d \u222b1nf \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 \u2a7d a1+ &#8230; + an\u22121\u3002 {displaystyle a_ {2} +ldots +a_ {n} leqslant int limits _ {1}^{n} f\uff08x\uff09\u3001mathrm {d} xleqslant a_ {1} +ldots +a_ {n-1}\u3002}}} \u7a4d\u5206\uff08i\uff09\u304c\u53ce\u675f\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u90e8\u5206\u7a4d\u5206 (\u222b1kf \uff08 \u30d0\u30c4 \uff09\uff09 d\u30d0\u30c4 )k=1\u221e{displaystyle {bigg\uff08} int limits _ {1}^{k} f\uff08x\uff09\u3001mathrm {d} x {bigg\uff09} _ {k = 1}^{infty}}} \u9650\u3089\u308c\u3066\u3044\u308b\u306e\u3067\u3001\u90e8\u5206\u7684\u306a\u5408\u8a08\u306e\u9650\u3089\u308c\u305f\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f15\u304d\u4ed8\u3051\u308b (\u2211j=1kaj)k=1\u221e{displaystyle {bigg\uff08} sum _ {j = 1}^{k} a_ {j} {bigg\uff09} _ {k = 1}^{infty}}} \u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u3002\u3053\u306e\u6587\u5b57\u5217\u3082\u975evanishing\u3067\u3059\uff08\u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u306e\u5358\u8a9e\u304c\u975e\u9670\u6027\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u3066\uff09\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9650\u3089\u308c\u305f\u975evanish\u306e\u5b9f\u6570\u306e\u6587\u5b57\u5217\u3068\u3057\u3066\u53ce\u675f\u3059\u308b\u305f\u3081\u3001\u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u306f\u53ce\u675f\u3057\u307e\u3059\u3002 \u30b7\u30ea\u30fc\u30ba\uff08a\uff09\u304c\u53ce\u675f\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u90e8\u5206\u7a4d\u5206\u306e\u4e0a\u8a18\u306e\u5b9a\u7fa9\u90e8\u5206\u3082\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5b9f\u6570\u306e\u9650\u5b9a\u7684\u304b\u3064\u975e\u6d88\u5316\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u53ce\u675f\uff08\u7a4d\u5206\uff08i\uff09\u306b\uff09 [7] \u3002 \u2211n=m\u221e1ns{displaystyle sum _ {n = m}^{infty} {frac {1} {n^{s}}}}} \u306e\u305f\u3081\u306b\u53ce\u675f\u3057\u307e\u3059 1.}&#8221;>\u78ba\u304b\u306b\u3001\u6a5f\u80fd f \uff08 \u30d0\u30c4 \uff09\uff09 = x\u2212s{displaystyle f\uff08x\uff09= x^{ &#8211;  s}} \u305d\u308c\u306f\u30d7\u30e9\u30b9\u3067\u3042\u308a\u3001\u7bc4\u56f2\u304c\u6e1b\u5c11\u3057\u307e\u3059 [ \u521d\u3081 \u3001 \u221e \uff09\uff09 \u3001 {displaystyle [1\u3001infty\uff09\u3001} \u3057\u305f\u304c\u3063\u3066\u3001\u7a4d\u5206\u57fa\u6e96\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 \u222bm\u221edxxs=\u222bm\u221ex\u2212sdx=[x\u2212s+1\u2212s+1]m\u221e=limx\u2192\u221e\u00a0x\u2212s+1\u2212s+1\u2212m\u2212s+1\u2212s+1=\u2212m\u2212s+1\u2212s+1,{displaystyle int limits _ {m}^{infty} {frac {mathrm {d} x} {x^{s}}} = int limits _ {m}^{infty} {x^{ &#8211;  s} mathrm {d} x}} =\u5de6[{x^-{x^-{x^-{x^-{x^-{x^-{x^-{x^-{x^-{x}}\u53f3] _ {m}^{infty} = lim _ {xto infty}\u301c{frac {x^{ &#8211;  s+1}} { &#8211;  s+1}}  &#8211;  {frac { &#8211;  s+1}}} { &#8211;  s+1}}}}}} \u3044\u3064  &#8211;  s + \u521d\u3081 < 0 \u3001 {displaystyle -s+1 1}&#8221;>[7] \u3002 \u2211n=2\u221e1n\u22c5(ln\u2061n)s{displaystyle sum _ {n = 2}^{infty} {frac {1} {ncdot\uff08ln n\uff09^{s}}}}}} \u306e\u305f\u3081\u306b\u53ce\u675f\u3057\u307e\u3059 1}&#8221;>\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u5206\u5c90\u3057\u307e\u3059\u3002\u78ba\u304b\u306b\u3001\u610f\u5473 f(x)=1x\u22c5(ln\u2061x)s(x\u2a7e2),{displaystyle f\uff08x\uff09= {frac {1} {xcdot\uff08ln x\uff09^{s}}} quad\uff08xgeqslant 2\uff09\u3001} \u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059 \u222bf(x)dx=(ln\u2061x)1\u2212s1\u2212s+C,s\u22601,{displaystyle int f\uff08x\uff09\u3001mathrm {d} x = {frac {\uff08ln x\uff09^{1-s}} {1-s}}+c\u3001quad sneq 1\u3001} \u222bf(x)dx=ln\u2061(ln\u2061x)+C,s=1,{displaystyle int f\uff08x\uff09\u3001mathrm {d} x = ln\uff08ln x\uff09+c\u3001quad s = 1\u3001} \u3057\u305f\u304c\u3063\u3066\u3001\u4e0d\u9069\u5207\u306a\u7a4d\u5206 \u222b2\u221ef(x)dx{displaystyle textytytt ir _ {{infty} f\uff08x\uff09\u3001matrm {d} x} x} \u3044\u3064\u5b58\u5728\u3057\u307e\u3059 1}&#8221;>\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u5b58\u5728\u3057\u307e\u305b\u3093 [8] \u3002 \u2191   \u30b9\u30d7\u30eb\u30fc\u30b9\u30a6\u30c3\u30c91966 < \u3001s\u3002 242\u3002  \u2191   Petrovic 2014\u2193 \u3001s\u3002 178\u3002  \u2191  C.\u30de\u30af\u30e9\u30a6\u30ea\u30f3\u3001 \u30d5\u30e9\u30ad\u30b7\u30aa\u30f3\u306e\u8ad6\u6587 \u30011\u3002\u30a8\u30c7\u30a3\u30f3\u30d0\u30e9\u30011742\u3002  \u2191  A.L. Cauchy\u3001\u30b7\u30ea\u30fc\u30ba\u306e\u53ce\u675f\u306b\u3064\u3044\u3066\u3001 \u5b8c\u5168\u306a\u4f5c\u54c1ser\u3002  2 \u30017\u3001Gauthier-Villars\uff081889\uff09\u3001s\u3002 267\u2013279\u3002  \u2191   \u30b9\u30d7\u30eb\u30fc\u30b9\u30a6\u30c3\u30c91966 < \u3001s\u3002 243\u3002  \u2191   \u30b9\u30d7\u30eb\u30fc\u30b9\u30a6\u30c3\u30c91966 < \u3001s\u3002 244\u3002  \u2191 a b   \u8a31\u53ef1971\u2193 \u3001s\u3002 276\u3002  \u2191   \u8a31\u53ef1971\u2193 \u3001s\u3002 276\u2013277\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\/15703#breadcrumbitem","name":"\u7d71\u5408\u57fa\u6e96-Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178"}}]}]