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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 Multivariate gamma function ： ウィキペディア英語版 Multivariate gamma function In mathematics, the multivariate gamma function, Γ''p''(·), is a generalization of the gamma function. It is useful in multivariate statistics, appearing in the probability density function of the Wishart and inverse Wishart distributions. It has two equivalent definitions. One is :$$ \Gamma_p(a)= \int_ \exp\left( -(S)\right) \left|S\right|^ dS , where S>0 means S is positive-definite. The other one, more useful in practice, is :$$ \Gamma_p(a)= \pi^\prod_^p \Gamma\left(a+(1-j)/2\right ). From this, we have the recursive relationships: :$$ \Gamma_p(a) = \pi^ \Gamma(a) \Gamma_(a-\tfrac) = \pi^ \Gamma_(a) \Gamma() . Thus * $\backslash Gamma\_1(a)=\backslash Gamma(a)$ * $\backslash Gamma\_2(a)=\backslash pi^\backslash Gamma(a)\backslash Gamma(a-1/2)$ * $\backslash Gamma\_3(a)=\backslash pi^\backslash Gamma(a)\backslash Gamma(a-1/2)\backslash Gamma(a-1)$ and so on. == Derivatives == We may define the multivariate digamma function as :$\backslash psi\_p(a)\; =\; \backslash frac\; =\; \backslash sum\_^p\; \backslash psi(a+(1-i)/2)\; ,$ and the general polygamma function as :$\backslash psi\_p^(a)\; =\; \backslash frac\; =\; \backslash sum\_^p\; \backslash psi^(a+(1-i)/2).$ 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「Multivariate 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.