[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/7843#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/7843","headline":"\u30ea\u30fc\u30b9\u51fd\u6570 – Wikipedia","name":"\u30ea\u30fc\u30b9\u51fd\u6570 – Wikipedia","description":"\u6570\u5b66\u306b\u304a\u3044\u3066\u30ea\u30fc\u30b9\u51fd\u6570\uff08\u30ea\u30fc\u30b9\u304b\u3093\u3059\u3046\u3001\u82f1: Riesz function\uff09\u3068\u306f\u3001\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3068\u306e\u95a2\u4fc2\u3067\u30ea\u30fc\u30b9\u30fb\u30de\u30eb\u30c4\u30a7\u30eb\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u3001\u6b21\u306e\u51aa\u7d1a\u6570\u3067\u4e0e\u3048\u3089\u308c\u308b\u6574\u51fd\u6570\u306e\u3053\u3068\u3092\u8a00\u3046\uff1a Riesz(x)=\u2212\u2211k=1\u221e(\u2212x)k(k\u22121)!\u03b6(2k).{displaystyle {rm {Riesz}}(x)=-sum _{k=1}^{infty }{frac {(-x)^{k}}{(k-1)!zeta (2k)}}.} F(x)=12Riesz(4\u03c02x){displaystyle F(x)={frac {1}{2}}{rm {Riesz}}(4pi ^{2}x)} \u3068\u3059\u308c\u3070\u3001\u53cc\u66f2\u4f59\u63a5\u306e\u30bc\u30ed\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u30ed\u30fc\u30e9\u30f3\u7d1a\u6570\u5c55\u958b\u306e\u4fc2\u6570\u3068\u3057\u3066\u305d\u308c\u306f\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3082\u3057 x2coth\u2061x2=\u2211n=0\u221ecnxn=1+112x2\u22121720x4+\u22ef{displaystyle {frac {x}{2}}coth {frac","datePublished":"2018-01-30","dateModified":"2018-01-30","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?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\/22eef2e96c1342079eb73b5a216d60b31c5d6689","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/22eef2e96c1342079eb73b5a216d60b31c5d6689","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/7843","about":["Wiki"],"wordCount":8194,"articleBody":"\u6570\u5b66\u306b\u304a\u3044\u3066\u30ea\u30fc\u30b9\u51fd\u6570\uff08\u30ea\u30fc\u30b9\u304b\u3093\u3059\u3046\u3001\u82f1: Riesz function\uff09\u3068\u306f\u3001\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3068\u306e\u95a2\u4fc2\u3067\u30ea\u30fc\u30b9\u30fb\u30de\u30eb\u30c4\u30a7\u30eb\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u3001\u6b21\u306e\u51aa\u7d1a\u6570\u3067\u4e0e\u3048\u3089\u308c\u308b\u6574\u51fd\u6570\u306e\u3053\u3068\u3092\u8a00\u3046\uff1aRiesz(x)=\u2212\u2211k=1\u221e(\u2212x)k(k\u22121)!\u03b6(2k).{displaystyle {rm {Riesz}}(x)=-sum _{k=1}^{infty }{frac {(-x)^{k}}{(k-1)!zeta (2k)}}.}  F(x)=12Riesz(4\u03c02x){displaystyle F(x)={frac {1}{2}}{rm {Riesz}}(4pi ^{2}x)} \u3068\u3059\u308c\u3070\u3001\u53cc\u66f2\u4f59\u63a5\u306e\u30bc\u30ed\u3092\u4e2d\u5fc3\u3068\u3057\u305f\u30ed\u30fc\u30e9\u30f3\u7d1a\u6570\u5c55\u958b\u306e\u4fc2\u6570\u3068\u3057\u3066\u305d\u308c\u306f\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u3082\u3057  x2coth\u2061x2=\u2211n=0\u221ecnxn=1+112x2\u22121720x4+\u22ef{displaystyle {frac {x}{2}}coth {frac {x}{2}}=sum _{n=0}^{infty }c_{n}x^{n}=1+{frac {1}{12}}x^{2}-{frac {1}{720}}x^{4}+cdots }\u3067\u3042\u308b\u306a\u3089\u3001F \u306f\u6b21\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3002F(x)=\u2211k=1\u221exkc2k(k\u22121)!=12x\u2212720x2+15120x3\u2212\u22ef{displaystyle F(x)=sum _{k=1}^{infty }{frac {x^{k}}{c_{2k}(k-1)!}}=12x-720x^{2}+15120x^{3}-cdots }\u03b6(2k) \u306e\u5024\u306f k \u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066 1 \u306b\u8fd1\u4ed8\u304d\u3001\u30ea\u30fc\u30b9\u51fd\u6570\u306b\u5bfe\u3059\u308b\u7d1a\u6570\u3092   x\u00a0exp\u2061(\u2212x){displaystyle x exp(-x)} \u306b\u5bfe\u3059\u308b\u7d1a\u6570\u3068\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3067\u3001\u305d\u308c\u306f\u6574\u51fd\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002\u307e\u305f F \u306fF(x)=\u2211k=1\u221ekk+1\u00afxkB2k\u00a0{displaystyle F(x)=sum _{k=1}^{infty }{frac {k^{overline {k+1}}x^{k}}{B_{2k}}} }\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3053\u3068\u3082\u3042\u308b\u3002nk\u00af{displaystyle n^{overline {k}}} \u306f\u30c9\u30ca\u30eb\u30c9\u30fb\u30af\u30cc\u30fc\u30b9\u306e\u8a18\u6cd5\u306b\u304a\u3051\u308b\u4e0a\u6607\u968e\u4e57\u3067\u3042\u308a\u3001Bn \u306f\u30d9\u30eb\u30cc\u30fc\u30a4\u6570\u3067\u3042\u308b\u3002\u3053\u306e\u7d1a\u6570\u306f\u4ee3\u66ff\u7684\u306a\u9805\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u51fd\u6570\u306f x \u304c\u8ca0\u306e\u65b9\u5411\u306b\u5897\u5927\u3059\u308b\u306b\u3064\u308c\u3066\u8ca0\u306e\u7121\u9650\u5927\u3078\u3068\u767a\u6563\u3059\u308b\u3002\u6b63\u306e x \u306b\u3064\u3044\u3066\u306f\u3088\u308a\u8208\u5473\u6df1\u304f\u3001\u7e4a\u7d30\u306a\u554f\u984c\u3068\u306a\u308b\u3002Table of Contents\u30ea\u30fc\u30b9\u6307\u6a19[\u7de8\u96c6]\u30ea\u30fc\u30b9\u51fd\u6570\u306e\u30e1\u30ea\u30f3\u5909\u63db[\u7de8\u96c6]\u30ea\u30fc\u30b9\u51fd\u6570\u306e\u8a08\u7b97[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u30ea\u30fc\u30b9\u6307\u6a19[\u7de8\u96c6]1\/2 \u3088\u308a\u5927\u304d\u3044\u4efb\u610f\u306e\u51aa\u4e57 e \u306b\u5bfe\u3057\u3066\u3001\u6b21\u304c\u6210\u7acb\u3059\u308b\u3002Riesz\u2061(x)=O(xe)(as\u00a0x\u2192\u221e){displaystyle operatorname {Riesz} (x)=O(x^{e})qquad ({text{as }}xto infty )}\u305f\u3060\u3057\u3053\u306e\u53f3\u8fba\u306f\u30e9\u30f3\u30c0\u30a6\u306e\u8a18\u53f7\u3067\u3042\u308a\u3001\u5024\u306f\u6b63\u304a\u3088\u3073\u8ca0\u306e\u3044\u305a\u308c\u306e\u65b9\u5411\u306b\u3064\u3044\u3066\u3082\u8003\u3048\u3089\u308c\u3066\u3044\u308b\u3002\u30ea\u30fc\u30b9\u306f\u3001\u4e0a\u306e\u5f0f\u304c 1\/4 \u3088\u308a\u5927\u304d\u3044\u4efb\u610f\u306e e \u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u3064\u3053\u3068\u306f\u30ea\u30fc\u30de\u30f3\u4e88\u60f3\u3068\u540c\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u305f[1]\u3002\u305f\u3060\u3057\u305d\u306e\u540c\u3058\u8ad6\u6587\u306b\u304a\u3044\u3066\u306f\u3001\u3084\u3084\u60b2\u89b3\u7684\u306a\u6b21\u306e\u6ce8\u91c8\u3082\u898b\u3089\u308c\u308b \u00abJe ne sais pas encore decider si cette condition facilitera la v\u00e9rification de l’hypoth\u00e8se\u00bb\u3002\u30ea\u30fc\u30b9\u51fd\u6570\u306e\u30e1\u30ea\u30f3\u5909\u63db[\u7de8\u96c6]\u30ea\u30fc\u30b9\u51fd\u6570\u306f\u3001\u30e1\u30ea\u30f3\u5909\u63db\u3092\u4ecb\u3057\u3066\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u51fd\u6570\u3068\u95a2\u9023\u4ed8\u3051\u3089\u308c\u308b\u3002\u4ecaM(Riesz(z))=\u222b0\u221eRiesz(z)zsdzz{displaystyle {mathbf {M} }({rm {Riesz}}(z))=int _{0}^{infty }{rm {Riesz(z)}}z^{s}{frac {dz}{z}}}\u3068\u3059\u308c\u3070\u3001"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki2\/archives\/7843#breadcrumbitem","name":"\u30ea\u30fc\u30b9\u51fd\u6570 – Wikipedia"}}]}]