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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 Particular values of the Gamma function ： ウィキペディア英語版 Particular values of the Gamma function The Gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series, and recurrence relations. ==Integers and half-integers== For positive integer arguments, the Gamma function coincides with the factorial, that is, :$\backslash Gamma(n)\; =\; (n-1)!\backslash qquad\; n\; \backslash in\; \backslash mathbb\_0,$ and hence :$\backslash begin$ \Gamma(1) &= 1, \\ \Gamma(2) &= 1, \\ \Gamma(3) &= 2, \\ \Gamma(4) &= 6, \\ \Gamma(5) &= 24. \end For non-positive integers, the Gamma function is not defined. For positive half-integers, the function values are given exactly by :$\backslash Gamma\; \backslash left\; (\backslash tfrac\; \backslash right)\; =\; \backslash sqrt\; \backslash pi\; \backslash frac$ \Gamma\left(\tfrac+n\right) &= \frac\, \sqrt = \frac \sqrt \\ \Gamma\left(\tfrac-n\right) &= \frac\, \sqrt = \frac \sqrt \end where ''n''!! denotes the double factorial. In particular, : \sqrt\, |$\backslash approx\; 0.8862269254527580137\backslash ,,$ | |- |$\backslash Gamma(\backslash tfrac52)\backslash ,$ |$=\; \backslash frac\; \backslash sqrt\backslash ,$ |$\backslash approx\; 1.3293403881791370205\backslash ,,$ | |- |$\backslash Gamma(\backslash tfrac72)\backslash ,$ |$=\; \backslash frac\; \backslash sqrt\backslash ,$ |$\backslash approx\; 3.3233509704478425512\backslash ,,$ | |} and by means of the reflection formula, : \sqrt\, |$\backslash approx\; 2.3632718012073547031\backslash ,,$ | |- |$\backslash Gamma(-\backslash tfrac52)\backslash ,$ |$=\; -\backslash frac\; \backslash sqrt\backslash ,$ |$\backslash approx\; -0.9453087204829418812\backslash ,,$ | |} 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「Particular values of the Gamma function」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.