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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 Looman–Menchoff theorem ： ウィキペディア英語版 Looman–Menchoff theorem In the mathematical field of complex analysis, the Looman–Menchoff theorem states that a continuous complex-valued function defined in an open set of the complex plane is holomorphic if and only if it satisfies the Cauchy–Riemann equations. It is thus a generalization of a theorem by Édouard Goursat, which instead of assuming the continuity of ''f'', assumes its Fréchet differentiability when regarded as a function from a subset of R2 to R2. A complete statement of the theorem is as follows: * Let Ω be an open set in C and ''f'' : Ω → C a continuous function. Suppose that the partial derivatives $\backslash partial\; f/\backslash partial\; x$ and $\backslash partial\; f/\backslash partial\; y$ exist everywhere but a countable set in Ω. Then ''f'' is holomorphic if and only if it satisfies the Cauchy–Riemann equation: ::$\backslash frac\backslash left(\backslash frac\; +\; i\backslash frac\backslash right)=0.$ ==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「Looman–Menchoff 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.