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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 Littlewood's Tauberian theorem ： ウィキペディア英語版 Littlewood's Tauberian theorem In mathematics, Littlewood's Tauberian theorem is a strengthening of Tauber's theorem introduced by . ==Statement== Littlewood showed the following: If ''a''''n'' = O(1/''n'' ), and as ''x'' ↑ 1 we have :$\backslash sum\; a\_n\; x^n\; \backslash to\; s,$ then :$\backslash sum\; a\_n\; =\; s.$ Hardy and Littlewood later showed that the hypothesis on ''a''''n'' could be weakened to the "one-sided" condition ''a''''n'' ≥ –''C''/''n'' for some constant ''C''. However in some sense the condition is optimal: Littlewood showed that if ''c''''n'' is any unbounded sequence then there is a series with |''a''''n''| ≤ |''c''''n''|/''n'' which is divergent but Abel summable. 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「Littlewood's Tauberian 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.