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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 Stieltjes transformation ： ウィキペディア英語版 Stieltjes transformation In mathematics, the Stieltjes transformation ''S''ρ(''z'') of a measure of density ρ on a real interval ''I'' is the function of the complex variable ''z'' defined outside ''I'' by the formula :$S\_(z)=\backslash int\_I\backslash frac,\; \backslash qquad\; t\; \backslash in\; I\; \backslash subset\; \backslash mathbb,\; \backslash ;\; z\; \backslash in\; \backslash mathbb\; \backslash backslash\; \backslash mathbb$ Under certain conditions we can reconstitute the density function ρ starting from its Stieltjes transformation thanks to the inverse formula of Stieltjes-Perron. For example, if the density ρ is continuous throughout ''I'', one will have inside this interval :$\backslash rho(x)=\backslash underset(x-i\backslash varepsilon)-S\_(x+i\backslash varepsilon)\}.$ ==Connections with moments of measures== (詳細はmoments of any order defined for each integer by the equality :$m\_=\backslash int\_I\; t^n\backslash ,\backslash rho(t)\backslash ,dt,$ then the Stieltjes transformation of ρ admits for each integer ''n'' the asymptotic expansion in the neighbourhood of infinity given by :$S\_(z)=\backslash sum\_^\backslash frac(z)=\backslash sum\_^\backslash frac\{z^\{n+1\}\}.$ 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「Stieltjes transformation」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.