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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 Sokhotski–Plemelj theorem ： ウィキペディア英語版 Sokhotski–Plemelj theorem The Sokhotski–Plemelj theorem (Polish spelling is ''Sochocki'') is a theorem in complex analysis, which helps in evaluating certain integrals. The real-line version of it (see below) is often used in physics, although rarely referred to by name. The theorem is named after Julian Sochocki, who proved it in 1868, and Josip Plemelj, who rediscovered it as a main ingredient of his solution of the Riemann-Hilbert problem in 1908. == Statement of the theorem == Let ''C'' be a smooth closed simple curve in the plane, and ''φ'' an analytic function on ''C''. Then the Cauchy-type integral :$\backslash frac\; \backslash int\_C\backslash frac,$ defines two analytic functions of ''z'', ''φ''i inside ''C'' and ''φ''e outside. Sokhotski–Plemelj formulas relate the boundary values of these two analytic functions at a point ''z'' on ''C'' and the Cauchy principal value $\backslash mathcal$ of the integral: :$\backslash phi\_i(z)=\backslash frac\backslash mathcal\backslash int\_C\backslash frac+\backslash frac\backslash varphi(z),\; \backslash ,$ :$\backslash phi\_e(z)=\backslash frac\backslash mathcal\backslash int\_C\backslash frac-\backslash frac\backslash varphi(z).\; \backslash ,$ Subsequent generalizations relaxed the smoothness requirements on curve ''C'' and the function ''φ''. 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「Sokhotski–Plemelj theorem」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.