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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 Hurwitz's theorem (complex analysis) ： ウィキペディア英語版 Hurwitz's theorem (complex analysis) In mathematics and in particular the field of complex analysis, Hurwitz's theorem is a theorem associating the zeroes of a sequence of holomorphic, compact locally uniformly convergent functions with that of their corresponding limit. The theorem is named after Adolf Hurwitz. ==Theorem statement== Let be a sequence of holomorphic functions on a connected open set ''G'' that converge uniformly on compact subsets of ''G'' to a holomorphic function ''f''. If ''f'' has a zero of order ''m'' at ''z''0 then for every small enough ρ > 0 and for sufficiently large ''k'' ∈ N (depending on ρ), ''fk'' has precisely ''m'' zeroes in the disk defined by |''z''−''z''0| < ρ, including multiplicity. Furthermore, these zeroes converge to ''z''0 as ''k'' → ∞. 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「Hurwitz's theorem (complex analysis)」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.