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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 Hypergeometric function identities ： ウィキペディア英語版 Wilf–Zeilberger pair In mathematics, specifically combinatorics, a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. WZ pairs are named after Herbert S. Wilf and Doron Zeilberger, and are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series. A function's WZ counterpart may be used to find an equivalent, and much simpler sum. Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a sure method to find a function's WZ counterpart, and can be implemented in a symbolic manipulation program. ==Definition== Two functions, ''F'' and ''G'', form a pair if and only if the following two conditions hold: : $F(n+1,k)-F(n,k)\; =\; G(n,k+1)-G(n,k)\backslash ,$ : $\backslash lim\_G(n,M)\; =\; 0.\; \backslash ,$ Together, these conditions ensure that the sum : $\backslash sum\_^\backslash infty\; ()\; =\; 0$ because the function ''G'' telescopes: :$\backslash begin\; \backslash sum\_^\backslash infty\; ()$ & ^M() \\ & ^M () \\ & = 0-0 \\ & {} = 0. \end{align} If ''F'' and ''G'' form a WZ pair, then they satisfy the relation : $G(n,k)\; =\; R(n,k)\; F(n,k),$ where $R(n,k)$ is a rational function of ''n'' and ''k'' and is called the ''WZ proof certificate''. 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「Wilf–Zeilberger pair」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.