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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 Poussin proof ： ウィキペディア英語版 Poussin proof In number theory, the Poussin proof is the proof of an identity related to the fractional part of a ratio. In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to η: :$\backslash frac\; \backslash approx\; \backslash ln\; \backslash eta\; +\; 2\backslash gamma\; -\; 1,$ where ''d'' represents the divisor function, and γ represents the Euler-Mascheroni constant. In 1898, Charles Jean de la Vallée-Poussin proved that if a large number η is divided by all the primes up to η, then the average fraction by which the quotient falls short of the next whole number is γ: :$\backslash frac\; \backslash right\; \backslash \}\}\; \backslash approx1-\; \backslash gamma,$ where represents the fractional part of ''x'', and π represents the prime-counting function. For example, if we divide 29 by 2, we get 14.5, which falls short of 15 by 0.5. ==References== *Dirichlet, G. L. "(Sur l'usage des séries infinies dans la théorie des nombres )", ''Journal für die reine und angewandte Mathematik'' 18 (1838), pp. 259–274. Cited in MathWorld article "Divisor Function" below. *de la Vallée Poussin, C.-J. Untitled communication. ''Annales de la Societe Scientifique de Bruxelles'' 22 (1898), pp. 84–90. Cited in MathWorld article "Euler-Mascheroni Constant" below. 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「Poussin proof」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.