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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 Rouché's theorem ： ウィキペディア英語版 Rouché's theorem Rouché's theorem, named after , states that if the complex-valued functions ''f'' and ''g'' are holomorphic inside and on some closed contour ''K'', with |''g''(''z'')| < |''f''(''z'')| on ''K'', then ''f'' and ''f'' + ''g'' have the same number of zeros inside ''K'', where each zero is counted as many times as its multiplicity. This theorem assumes that the contour ''K'' is simple, that is, without self-intersections. Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below. == Symmetric version == Theodor Estermann (1902–1991) proved in his book ''Complex Numbers and Functions'' the following statement: Let $K\backslash subset\; G$ be a bounded region with continuous boundary $\backslash partial\; K$. Two holomorphic functions $f,\backslash ,g\backslash in\backslash mathcal\; H(G)$ have the same number of roots (counting multiplicity) in $K$, if the strict inequality : holds on the boundary $\backslash partial\; K$. The original Rouché's theorem then follows by setting $f(z):=f(z)+g(z)$ and $g(z):=f(z)$. 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「Rouché's 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.