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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 Boggio's formula ： ウィキペディア英語版 Boggio's formula In the mathematical field of potential theory, Boggio's formula is an explicit formula for the Green's function for the polyharmonic Dirichlet problem on the ball of radius 1. It was discovered by the Italian mathematician Tommaso Boggio. The polyharmonic problem is to find a function ''u'' satisfying :$(-\backslash Delta)^m\; u(x)\; =\; f(x)$ where ''m'' is a positive integer, and $(-\backslash Delta)$ represents the Laplace operator. The Green's function is a function satisfying :$(-\backslash Delta)^m\; G(x,y)\; =\; \backslash delta(x-y)$ where $\backslash delta$ represents the Dirac delta distribution, and in addition is equal to 0 up to order ''m-1'' at the boundary. Boggio found that the Green's function on the ball in ''n'' spatial dimensions is :$G\_\; (x,y)\; =\; C\_\; |x-y|^\; \backslash int\_1^\backslash right|\}\}\; (v^2-1)^\; v^\; dv$ The constant $C\_$ is given by :$C\_\; =\backslash frac,$ where $e\_n\; =\; \backslash frac\}\})\}$ ==Sources== * * 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「Boggio's formula」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.