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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 Lévy's constant ： ウィキペディア英語版 Lévy's constant In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions.〔 〕 In 1935, the Soviet mathematician Aleksandr Khinchin showed〔 (given in Dover book ) "Zur metrischen Kettenbruchtheorie," ''Compositio Matlzematica'', 3, No.2, 275–285 (1936). 〕 that the denominators ''q''''n'' of the convergents of the continued fraction expansions of almost all real numbers satisfy :$\backslash lim\_^=\; \backslash gamma$ for some constant γ. Soon afterward, in 1936, the French mathematician Paul Lévy found〔 (given in Dover book ) P. Levy, ''Théorie de l'addition des variables aléatoires'', Paris, 1937, p. 320. 〕 the explicit expression for the constant, namely :$\backslash gamma\; =\; e^\; =\; 3.275822918721811159787681882\backslash ldots.$ The term "Lévy's constant" is sometimes used to refer to $\backslash pi^2/(12\backslash ln2)$ (the logarithm of the above expression), which is approximately equal to 1.1865691104…. The base-10 logarithm of Lévy's constant, which is approximately 0.51532041…, is half of the reciprocal of the limit in Lochs' theorem. ==See also== *Khinchin's constant 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「Lévy's 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.