翻訳と辞書 Words near each other ・ K-Verband ・ K-vertex-connected graph ・ K-Ville ・ K-Ville (TV series) ・ K-W Line ・ K-W United FC ・ K-W United FC (W-League) ・ K-Wagen ・ K-water ・ K-Way Merge Algorithms ・ K-X-P ・ K-Y Jelly ・ K-Z ・ K. (novel) ・ K-frame ・ K-function ・ K-Gee ・ K-graph C*-algebra ・ K-group ・ K-Hill (artist) ・ K-Hito ・ K-Hits ・ K-hole ・ K-homology ・ K-ID ・ K-independent hashing ・ K-index ・ K-index (meteorology) ・ K-Jee ・ K-K-K-Katy Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク K-function ： ウィキペディア英語版 K-function In mathematics, the K-function, typically denoted ''K''(''z''), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the Gamma function. Formally, the K-function is defined as :$K(z)=(2\backslash pi)^\; \backslash exp\backslash left(z\backslash \backslash \; 2\backslash end+\backslash int\_0^\; \backslash ln(t!)\backslash ,dt\backslash right).$ It can also be given in closed form as :$K(z)=\backslash exp\backslash left()$ where ζ'(''z'') denotes the derivative of the Riemann zeta function, ζ(''a'',''z'') denotes the Hurwitz zeta function and : :$K(z)=\backslash exp\backslash left(\backslash psi^(z)+\backslash frac-\backslash frac\; z2\; \backslash ln\; (2\backslash pi)\backslash right)$ Or using balanced generalization of Polygamma function:〔(Olivier Espinosa Victor H. Moll. A Generalized polygamma function. Integral Transforms and Special Functions Vol. 15, No. 2, April 2004, pp. 101–115 )〕 :$K(z)=A\; e^\}$ :where A is Glaisher constant. The K-function is closely related to the Gamma function and the Barnes G-function; for natural numbers ''n'', we have :$K(n)=\backslash frac.$ More prosaically, one may write :$K(n+1)=1^1\backslash ,\; 2^2\backslash ,\; 3^3\; \backslash cdots\; n^n.$ The first values are :1, 4, 108, 27648, 86400000, 4031078400000, 3319766398771200000, ... (). == References == 〔 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「K-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.