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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 Polygamma function ： ウィキペディア英語版 Polygamma function In mathematics, the polygamma function of order ''m'' is a meromorphic function on $\backslash C$ and defined as the (''m''+1)-th derivative of the logarithm of the gamma function: :$\backslash psi^(z)\; :=\; \backslash frac\; \backslash psi(z)\; =\; \backslash frac\}\; \backslash ln\backslash Gamma(z).$ Thus :$\backslash psi^(z)\; =\; \backslash psi(z)\; =\; \backslash frac$ holds where ψ(''z'') is the digamma function and Γ(''z'') is the gamma function. They are holomorphic on $\backslash C\; \backslash setminus\; -\backslash N\_0$. At all the nonpositive integers these polygamma functions have a pole of order ''m'' + 1. The function ψ(1)(''z'') is sometimes called the trigamma function. (z) |- | | | |- |$$ \psi^(z) |$$ \psi^(z) |$$ \psi^(z) |} ==Integral representation== The polygamma function may be represented as :$\backslash begin$ \psi^(z)&= (-1)^\int_0^\infty\frac}\ dt\\ &=-\int_0^1\frac\ln^mt\ dt \end which holds for Re ''z'' >0 and ''m'' > 0. For ''m'' = 0 see the digamma function definition. 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「Polygamma 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.