翻訳と辞書 Words near each other ・ Liouville dynamical system ・ Liouville field theory ・ Liouville function ・ Liouville gravity ・ Liouville number ・ Liouville Point ・ Liouville surface ・ Liouville's equation ・ Liouville's formula ・ Liouville's theorem ・ Liouville's theorem (complex analysis) ・ Liouville's theorem (conformal mappings) ・ Liouville's theorem (differential algebra) ・ Liouville's theorem (Hamiltonian) ・ Liouville–Arnold theorem ・ Liouville–Neumann series ・ Liouvillian function ・ Lioux ・ Lioux-les-Monges ・ Liow Tiong Lai ・ Lioxanthodes ・ Liozna ・ Liozna Raion ・ Lip ・ LIP (company) ・ Lip (disambiguation) ・ Lip (gastropod) ・ Lip augmentation ・ Lip balm ・ Lip compression Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Liouville–Neumann series ： ウィキペディア英語版 Liouville–Neumann series In mathematics, the Liouville–Neumann series is an infinite series that corresponds to the resolvent formalism technique of solving the Fredholm integral equations in Fredholm theory. ==Definition== The Liouville–Neumann series is defined as :$\backslash phi\backslash left(x\backslash right)\; =\; \backslash sum^\backslash infty\_\; \backslash lambda^n\; \backslash phi\_n\; \backslash left(x\backslash right)$ which is a unique, continuous solution of a Fredholm integral equation of the second kind: :$f(t)=\; \backslash phi(t)\; -\; \backslash lambda\; \backslash int\_a^bK(t,s)\backslash phi(s)\backslash ,ds.$ If the ''n''th iterated kernel is defined as :$K\_n\backslash left(x,z\backslash right)\; =\; \backslash int\backslash int\backslash cdots\backslash int\; K\backslash left(x,y\_1\backslash right)K\backslash left(y\_1,y\_2\backslash right)\; \backslash cdots\; K\backslash left(y\_,\; z\backslash right)\; dy\_1\; dy\_2\; \backslash cdots\; dy\_$ then :$\backslash phi\_n\backslash left(x\backslash right)\; =\; \backslash int\; K\_n\backslash left(x,z\backslash right)f\backslash left(z\backslash right)dz$ with :$\backslash phi\_0\backslash left(x\backslash right)\; =\; f\backslash left(x\backslash right).$ The resolvent or solving kernel is given by :$K\backslash left(x,\; z;\backslash lambda\backslash right)\; =\; \backslash sum^\backslash infty\_\; \backslash lambda^n\; K\_\; \backslash left(x,\; z\backslash right).$ The solution of the integral equation becomes :$\backslash phi\backslash left(x\backslash right)\; =\; \backslash int\; K\; \backslash left(\; x,\; z;\backslash lambda\backslash right)\; f\backslash left(z\backslash right)dz.$ Similar methods may be used to solve the Volterra equations. 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「Liouville–Neumann series」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.