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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 Gauss's constant ： ウィキペディア英語版 Gauss's constant In mathematics, Gauss' constant, denoted by ''G'', is defined as the reciprocal of the arithmetic-geometric mean of 1 and the square root of 2: : $G\; =\; \backslash frac)\}\; =\; 0.8346268\backslash dots.$ The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered that : $G\; =\; \backslash frac\backslash int\_0^1\backslash fracB(\; \backslash tfrac,\; \backslash tfrac)$ where ''B'' denotes the beta function. Gauss' constant should not be confused with the Gaussian gravitational constant. ==Relations to other constants== Gauss' constant may be used to express the Gamma function at argument 1/4: : $\backslash Gamma(\; \backslash tfrac)\; =\; \backslash sqrt$ Alternatively, : $G\; =\; \backslash frac)\; )^2\}\{2\backslash sqrt\{\; 2\backslash pi^3\}\}$ and since π and Γ(1/4) are algebraically independent with Γ(1/4) irrational, Gauss' constant is transcendental. 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「Gauss'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.