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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 Infinite arithmetic series ： ウィキペディア英語版 Infinite arithmetic series In mathematics, an infinite arithmetic series is an infinite series whose terms are in an arithmetic progression. Examples are and . The general form for an infinite arithmetic series is :$\backslash sum\_^\backslash infty(an+b).$ If ''a'' = ''b'' = 0, then the sum of the series is 0. If either ''a'' or ''b'' is nonzero while the other is, then the series diverges and has no sum in the usual sense. ==Zeta regularization== The zeta-regularized sum of an arithmetic series of the right form is a value of the associated Hurwitz zeta function, :$\backslash sum\_^\backslash infty(n+\backslash beta)\; =\; \backslash zeta\_H\; (-1;\; \backslash beta).$ Although zeta regularization sums 1 + 1 + 1 + 1 + · · · to ζR(0) = −1⁄2 and to ζR(−1) = −1⁄12, where ζ is the Riemann zeta function, the above form is ''not'' in general equal to :$-\backslash frac\; -\; \backslash frac.$ 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「Infinite arithmetic series」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.