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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 Gompertz constant ： ウィキペディア英語版 Gompertz constant In mathematics, the Gompertz constant or Euler-Gompertz constant, denoted by $G$, appears in integral evaluations and as a value of special functions. It is named after B. Gompertz. It can be defined by the continued fraction : $G\; =\; \backslash frac\}\}\}\}\}\}\}\; ,$ or, alternatively, by : $G\; =\; \backslash frac\}\}\}\}\}\}\}.$ The most frequent appearance of $G$ is in the following integrals: : $G\; =\; \backslash int\_0^\backslash infty\backslash ln(1+x)e^dx=\backslash int\_0^\backslash infty\backslash fracdx=\backslash int\_0^1\backslash fracdx.$ The numerical value of $G$ is about : $G\; =\; 0.596347362323194074341078499369279376074\backslash dots$ During the studying divergent infinite series Euler met with $G$ via, for example, the above integral representations. Le Lionnais called $G$ as Gompertz constant by its role in survival analysis.〔 ==Identities involving the Gompertz constant== The constant $G$ can be expressed by the exponential integral as : $G\; =\; -e\backslash textrm(-1).$ Applying the Taylor expansion of $\backslash textrm$ we have that : $G\; =\; -e\backslash left(\backslash gamma+\backslash sum\_^\backslash infty\backslash frac\backslash right).$ Gompertz's constant is connected to the Gregory coefficients via the 2013 formula of I. Mező: : $G\; =\; \backslash sum\_^\backslash infty\backslash frac-\backslash sum\_^\backslash infty\; C\_\backslash -\backslash frac.$ 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「Gompertz 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.