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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 Erdős–Borwein constant ： ウィキペディア英語版 Erdős–Borwein constant The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein. By definition it is: :$E=\backslash sum\_^\backslash frac\backslash approx1.606695152415291763\backslash dots$ ==Equivalent forms== It can be proven that the following forms all sum to the same constant: :$$ E=\sum_^\frac :$$ E=\sum_^\sum_^ \frac^ \frac :$$ E=\sum_^\frac where σ0(''n'') = ''d''(''n'') is the divisor function, a multiplicative function that equals the number of positive divisors of the number ''n''. To prove the equivalence of these sums, note that they all take the form of Lambert series and can thus be resummed as such.〔The first of these forms is given by , ex. 27, p. 157; Knuth attributes the transformation to this form to an 1828 work of Clausen.〕 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「Erdős–Borwein constant」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.