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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 Reciprocal gamma function ： ウィキペディア英語版 Reciprocal gamma function In mathematics, the reciprocal gamma function is the function :$f(z)\; =\; \backslash frac,$ where Γ(''z'') denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire function. As an entire function, it is of order 1 (meaning that $\backslash log(\backslash log|1/\backslash Gamma(z)|)$ grows no faster than $\backslash log|z|$), but of infinite type (meaning that $\backslash log|1/\backslash Gamma(z)|$ grows faster than any multiple of |z|, since its growth is approximately proportional to $|z|\backslash log|z|$ in the left-hand plane). The reciprocal is sometimes used as a starting point for numerical computation of the gamma function, and a few software libraries provide it separately from the regular gamma function. Karl Weierstrass called the reciprocal gamma function the "factorielle" and used it in his development of the Weierstrass factorization theorem. ==Taylor series== Taylor series expansion around 0 gives :$\backslash frac\; =\; z\; +\; \backslash gamma\; z^2\; +\; \backslash left(\backslash frac\; -\; \backslash frac\backslash right)z^3\; +\; \backslash cdots$ where γ is the Euler–Mascheroni constant. For ''k'' > 2, the coefficient ''ak'' for the ''zk'' term can be computed recursively as :$a\_k\; =\; \backslash frac\}$ where ζ(''s'') is the Riemann zeta function. For small values, this gives the following values: 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「Reciprocal 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.