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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.〕 : for . Here ζ(''s'') denotes the Riemann zeta function and Γ(s) is the Gamma function. The functional equation (or reflection formula) for xi is : The upper-case Xi, Ξ, is defined by Landau (loc. cit., §71) as : and obeys the functional equation : 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
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