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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 Ursell function ： ウィキペディア英語版 Ursell function In statistical mechanics, an Ursell function or connected correlation function, is a cumulant of a random variable. It is also called a connected correlation function as it can often be obtained by summing over connected Feynman diagrams (the sum over all Feynman diagrams gives the correlation functions). The Ursell function was named after Harold Ursell, who introduced it in 1927. ==Definition== If ''X'' is a random variable, the moments ''s''''n'' and cumulants (same as the Ursell functions) ''u''''n'' are functions of ''X'' related by the exponential formula: : $\backslash operatorname\; E(\backslash exp(zX))\; =\; \backslash sum\_n\; s\_n\; \backslash frac\; =\; \backslash exp\backslash left(\backslash sum\_n\; u\_n\; \backslash frac\; \backslash right)$ (where E is the expectation). The Ursell functions for multivariate random variables are defined analogously to the above, and in the same way as multivariate cumulants. :$u\_n(X\_1,\backslash ldots,X\_n)\; =\; \backslash frac\backslash cdots\; \backslash frac\backslash log\; E(\backslash exp\backslash sum\; z\_iX\_i)\backslash big|\_$ The Ursell functions of a single random variable ''X'' are obtained from these by setting ''X''=''X''1=...=''X''''n''. The first few are given by :$u\_1(X\_1)=E(X\_1)$ :$u\_2(X\_1,X\_2)=E(X\_1X\_2)-E(X\_1)E(X\_2)$ :$u\_3(X\_1,X\_2,X\_3)=E(X\_1X\_2X\_3)-E(X\_1)E(X\_2X\_3)-E(X\_2)E(X\_3X\_1)-E(X\_3)E(X\_1X\_2)+2E(X\_1)E(X\_2)E(X\_3)$ 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「Ursell 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.