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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 Hypergeometric function of a matrix argument ： ウィキペディア英語版 Hypergeometric function of a matrix argument In mathematics, the hypergeometric function of a matrix argument is a generalization of the classical hypergeometric series. It is a function defined by an infinite summation which can be used to evaluate certain multivariate integrals. Hypergeometric functions of a matrix argument have applications in random matrix theory. For example, the distributions of the extreme eigenvalues of random matrices are often expressed in terms of the hypergeometric function of a matrix argument. ==Definition== Let $p\backslash ge\; 0$ and $q\backslash ge\; 0$ be integers, and let $X$ be an $m\backslash times\; m$ complex symmetric matrix. Then the hypergeometric function of a matrix argument $X$ and parameter $\backslash alpha>0$ is defined as : $$ _pF_q^(a_1,\ldots,a_p; b_1,\ldots,b_q;X) = \sum_^\infty\sum_ \frac\cdot \frac} } \cdot C_\kappa^(X), where $\backslash kappa\backslash vdash\; k$ means $\backslash kappa$ is a partition of $k$, $(a\_i)^\_$ is the Generalized Pochhammer symbol, and $C\_\backslash kappa^(X)$ is the "C" normalization of the Jack function. 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「Hypergeometric function of a matrix argument」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.