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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 Dixon's identity ： ウィキペディア英語版 Dixon's identity In mathematics, Dixon's identity (or Dixon's theorem or Dixon's formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating a hypergeometric sum. These identities famously follow from the MacMahon Master theorem, and can now be routinely proved by computer algorithms . ==Statements== The original identity, from , is :$\backslash sum\_^(-1)^^3\; =\backslash frac.$ A generalization, also sometimes called Dixon's identity, is :$\backslash sum\_^a(-1)^k\; =\; \backslash frac$ where ''a'', ''b'', and ''c'' are non-negative integers . The sum on the left can be written as the terminating well-poised hypergeometric series :$.$ This holds for Re(1 + ''a'' − ''b'' − ''c'') > 0. As ''c'' tends to −∞ it reduces to Kummer's formula for the hypergeometric function 2F1 at −1. Dixon's theorem can be deduced from the evaluation of the Selberg integral. 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「Dixon's identity」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.