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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kronecker limit formula ： ウィキペディア英語版 Kronecker limit formula In mathematics, the classical Kronecker limit formula describes the constant term at ''s'' = 1 of a real analytic Eisenstein series (or Epstein zeta function) in terms of the Dedekind eta function. There are many generalizations of it to more complicated Eisenstein series. It is named for Leopold Kronecker. ==First Kronecker limit formula== The (first) Kronecker limit formula states that :$E(\backslash tau,s)\; =\; +\; 2\backslash pi(\backslash gamma-\backslash log(2)-\backslash log(\backslash sqrt|\backslash eta(\backslash tau)|^2))\; +O(s-1),$ where *''E''(τ,''s'') is the real analytic Eisenstein series, given by :$E(\backslash tau,s)\; =\backslash sum\_\backslash prod\_(1-q^n)$, with ''q'' = e2π i τ is the Dedekind eta function. So the Eisenstein series has a pole at ''s'' = 1 of residue π, and the (first) Kronecker limit formula gives the constant term of the Laurent series at this pole. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kronecker limit formula」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.