{"id":1641,"date":"2011-01-06T01:12:52","date_gmt":"2011-01-05T16:12:52","guid":{"rendered":"http:\/\/njet.oops.jp\/wordpress\/?p=1641"},"modified":"2011-07-12T14:58:28","modified_gmt":"2011-07-12T05:58:28","slug":"polya-szego%e3%81%ae%e5%95%8f%e9%a1%8c%e9%9b%862","status":"publish","type":"post","link":"https:\/\/njet.oops.jp\/wordpress\/2011\/01\/06\/polya-szego%e3%81%ae%e5%95%8f%e9%a1%8c%e9%9b%862\/","title":{"rendered":"Polya-Szego\u306e\u554f\u984c\u96c6(2)"},"content":{"rendered":"<p><latex> \u672c\u306e\u6574\u7406\u306f\u305d\u3063\u3061\u306e\u3051\u3067 Polya-Szego<br \/>\n(\u30dd\u30ea\u30a2\uff06\u30bb\u30b2\u30fc)\u5171\u8457\u306e\u554f\u984c\u96c6\u3092\u8aad\u3093\u3067\u3044\u308b\u304c\uff0c\u4e45\u3057\u632f\u308a\u306b\u773a\u3081\u308b\u3068\u9762\u767d\u3044\u554f\u984c\u304c\u76ee\u767d\u62bc\u3057\u3060\u3002<br \/>\n\u6bd4\u8f03\u7684\u521d\u7b49\u7684\u3067\uff0c\u9762\u767d\u305d\u3046\u306a\u3082\u306e\u3092\u30d4\u30c3\u30af\u30a2\u30c3\u30d7\u3002 \\[<br \/>\nA_n=\\frac{1}{n+1}+\\frac{1}{n+2}+\\cdots+\\frac{1}{n+n} \\] \u304c $A=\\log<br \/>\n2$ \u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u306f\uff0c\u533a\u5206\u6c42\u7a4d\u6cd5(\u30ea\u30fc\u30de\u30f3\u548c)\u304b\u3089\u76f4\u3050\u306b\u5206\u304b\u308b\u3002\u3067\u306f\uff0c\u3069\u308c\u304f\u3089\u3044\u306e\u30b9\u30d4\u30fc\u30c9\u3067\u53ce\u675f\u3059\u308b\u3060\u308d\u3046\u304b\u3002Part II \u306e<br \/>\nNo.12 \u306b\u3088\u308c\u3070 \\[ \\lim_{n\\to\\infty} n(A-A_n)=\\frac{1}{4} \\]<br \/>\n\u304c\u6210\u308a\u7acb\u3064\u3089\u3057\u3044\u306e\u3067\u3042\u308b\u3002<br \/>\n\u3053\u308c\u306f\u7c21\u5358\u306b\u89e3\u3051\u305f\u3002\u30ea\u30fc\u30de\u30f3\u548c\u306f\u5fae\u5c0f\u9577\u65b9\u5f62\u306e\u548c\u306a\u306e\u3067\uff0c\u7a4d\u5206\u3092\u9577\u65b9\u5f62\u3067\u8fd1\u4f3c\u3057\u305f\u3068\u304d\u306e\u8aa4\u5dee\u8a55\u4fa1\u3092\u3059\u308c\u3070\u3088\u3044\u3002\u95a2\u6570$f(x)=\\frac{1}{1+x}$\u306f\u533a\u9593$0\\leq x\\leq 1$\u3067\u5358\u8abf\u6e1b\u5c11\u304b\u3064\u4e0b\u306b\u51f8\u3067\u3042\u308b\u304b\u3089\uff0c\u5404\u9577\u65b9\u5f62\u3067\u306e\u8aa4\u5dee\u306f\uff0c\u4e0a\u304b\u3089\u306f\u5f26\u3067\uff0c\u4e0b\u304b\u3089\u306f\u53f3\u7aef\u3067\u306e\u63a5\u7dda\u3067\u62bc\u3055\u3048\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u3002<br \/>\n\u4e0b\u304b\u3089\u306e\u548c\u306f\uff0c\u3053\u308c\u307e\u305f\u533a\u5206\u6c42\u7a4d\u6cd5\u3067\u4e0a\u304b\u3089\u62bc\u3055\u3048\u305f\u3082\u306e\u3068\u540c\u3058\u5024\u306b\u53ce\u675f\u3059\u308b\u3002\u305d\u3046\u3044\u3046\u308f\u3051\u3067\u3053\u306e\u5834\u5408\uff0c \\[<br \/>\n\\lim_{n\\to\\infty} n(A-A_n)=\\frac{1}{2} \\lbrace f(0)-f(1)\\rbrace<br \/>\n=\\frac{1}{4} \\] \u3068\u306a\u308b\u3002 <\/latex><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u306e\u6574\u7406\u306f\u305d\u3063\u3061\u306e\u3051\u3067 Polya-Szego (\u30dd\u30ea\u30a2\uff06\u30bb\u30b2\u30fc)\u5171\u8457\u306e\u554f\u984c\u96c6\u3092\u8aad\u3093\u3067\u3044\u308b\u304c\uff0c\u4e45\u3057\u632f\u308a\u306b\u773a\u3081\u308b\u3068\u9762\u767d\u3044\u554f\u984c\u304c\u76ee\u767d\u62bc\u3057\u3060\u3002 \u6bd4\u8f03\u7684\u521d\u7b49\u7684\u3067\uff0c\u9762\u767d\u305d\u3046\u306a\u3082\u306e\u3092\u30d4\u30c3\u30af\u30a2\u30c3\u30d7\u3002 \\[ A_n=\\frac{1}{n [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,11],"tags":[],"class_list":["post-1641","post","type-post","status-publish","format-standard","hentry","category-5","category-11"],"_links":{"self":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/1641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/comments?post=1641"}],"version-history":[{"count":17,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/1641\/revisions"}],"predecessor-version":[{"id":1829,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/posts\/1641\/revisions\/1829"}],"wp:attachment":[{"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/media?parent=1641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/categories?post=1641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/njet.oops.jp\/wordpress\/wp-json\/wp\/v2\/tags?post=1641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}