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In mathematics, the reciprocal gamma function is the function : 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 grows no faster than ), but of infinite type (meaning that grows faster than any multiple of |z|, since its growth is approximately proportional to 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 : where γ is the Euler–Mascheroni constant. For ''k'' > 2, the coefficient ''ak'' for the ''zk'' term can be computed recursively as : 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
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