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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 Riemann Xi function ： ウィキペディア英語版 Riemann Xi function In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named in honour of Bernhard Riemann. ==Definition== Riemann's original lower-case xi-function, ξ, has been renamed with an upper-case Xi, Ξ, by Edmund Landau (see below). Landau's lower-case xi, ξ, is defined as:〔Edmund Landau. Handbuch der Lehre von der Verteilung der Primzahlen, Teubner, Leipzig 1909. Third edition Chelsea, New York, 1974, §70.〕 :$\backslash xi(s)\; =\; \backslash tfrac\; s(s-1)\; \backslash pi^\; \backslash Gamma\backslash left(\backslash tfrac\; s\backslash right)\; \backslash zeta(s)$ for $s\backslash in\backslash Bbb$. Here ζ(''s'') denotes the Riemann zeta function and Γ(s) is the Gamma function. The functional equation (or reflection formula) for xi is :$\backslash xi(1-s)\; =\; \backslash xi(s).$ The upper-case Xi, Ξ, is defined by Landau (loc. cit., §71) as :$\backslash Xi(z)\; =\; \backslash xi(\backslash frac12+zi)$ and obeys the functional equation :$\backslash Xi(-z)\; =\backslash Xi(z).$ As reported by Landau (loc. cit., p. 894) this function Ξ is the function Riemann originally denoted by ξ. 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「Riemann Xi function」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.