翻訳と辞書 Words near each other ・ Abel transform ・ Abel Transon ・ Abel Trujillo ・ Abel Valdez ・ Abel Villanueva ・ Abel Vázquez ・ Abel Vázquez (sport shooter) ・ Abel Wolman ・ Abel Womack ・ Abel Woolrich ・ Abel Wornell ・ Abel Xavier ・ Abel Ávila ・ Abel's binomial theorem ・ Abel's identity ・ Abel's inequality ・ Abel's irreducibility theorem ・ Abel's Island ・ Abel's Island (film) ・ Abel's sum formula ・ Abel's summation formula ・ Abel's test ・ Abel's theorem ・ Abel, Alabama ・ Abel, King of Denmark ・ Abel, Lord of Langeland ・ Abel-beth-maachah ・ Abel-cheramim ・ Abel-Dominique Boyé ・ Abel-François Villemain Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Abel's inequality ： ウィキペディア英語版 Abel's inequality In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case. Let be a sequence of real numbers that is either nonincreasing or nondecreasing, and let be a sequence of real or complex numbers. If is nondecreasing, it holds that :$$ \left |\sum_^n a_k b_k \right | \le \operatorname_ |B_k| (|a_n| + a_n - a_1), and if is nonincreasing, it holds that :$$ \left |\sum_^n a_k b_k \right | \le \operatorname_ |B_k| (|a_n| - a_n + a_1), where :$$ B_k =b_1+\cdots+b_k. In particular, if the sequence is nonincreasing and nonnegative, it follows that :$$ \left |\sum_^n a_k b_k \right | \le \operatorname_ |B_k| a_1, Abel's inequality follows easily from Abel's transformation, which is the discrete version of integration by parts: If and are sequences of real or complex numbers, it holds that :$$ \sum_^n a_k b_k = a_n B_n - \sum_^ B_k (a_ - a_k). ==References== * * ''(''Abel's inequality'' )'' in ''Encyclopedia of Mathematics''. 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「Abel's inequality」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.