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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 Hadamard finite part integral ： ウィキペディア英語版 Hadamard regularization In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part, introduced by . showed that this can be interpreted as taking the meromorphic continuation of a convergent integral. If the Cauchy principal value integral : exists, then it may be differentiated with respect to to obtain the Hadamard finite part integral as follows: : Note that the symbols $\backslash mathcal$ and $\backslash mathcal$ are used here to denote Cauchy principal value and Hadamard finite-part integrals respectively. The Hadamard finite part integral above (for ) may also be given by the following equivalent definitions: : $\backslash mathcal\backslash int\_a^b\; \backslash frac\backslash ,\; dt\; =\; \backslash lim\_\; \backslash left\backslash \backslash ,dt\; +\; \backslash int\_^b\backslash frac\backslash ,dt\; -\backslash frac\backslash right\backslash \},$ : $\backslash mathcal\backslash int\_a^b\; \backslash frac\backslash ,\; dt\; =\; \backslash lim\_\; \backslash left\backslash f(t)\}$ \,dt -\frac-\frac(\frac-\frac)\right\}. The definitions above may be derived by assuming that the function is differentiable infinitely many times at , that is, by assuming that can be represented by its Taylor series about . For details, see . (Note that the term in the second equivalent definition above is missing in but this is corrected in the errata sheet of the book.) Integral equations containing Hadamard finite part integrals (with unknown) are termed hypersingular integral equations. Hypersingular integral equations arise in the formulation of many problems in mechanics, such as in fracture analysis. ==References== *. *. *. *. *. *. * 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「Hadamard regularization」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.