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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 Hyperharmonic number ： ウィキペディア英語版 Hyperharmonic number In mathematics, the ''n''-th hyperharmonic number of order ''r'', denoted by $H\_n^$, is recursively defined by the relations: : $H\_n^\; =\; \backslash frac\; ,$ and : $H\_n^\; =\; \backslash sum\_^n\; H\_k^\backslash quad(r>0).$ In particular, $H\_n=H\_n^$ is the ''n''-th harmonic number. The hyperharmonic numbers were discussed by J. H. Conway and R. K. Guy in their 1995 book ''The Book of Numbers''.〔 ==Identities involving hyperharmonic numbers== By definition, the hyperharmonic numbers satisfy the recurrence relation :$H\_n^\; =\; H\_^\; +\; H\_n^.$ In place of the recurrences, there is a more effective formula to calculate these numbers: : $H\_^=\backslash binom(H\_-H\_).$ The hyperharmonic numbers have a strong relation to combinatorics of permutations. The generalization of the identity : is an ''r''-Stirling number of the first kind. 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「Hyperharmonic number」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.