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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 summation by parts ： ウィキペディア英語版 summation by parts In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. The summation by parts formula is sometimes called Abel's lemma or Abel transformation. ==Statement== Suppose $\backslash$ and $\backslash$ are two sequences. Then, :$\backslash sum\_^n\; f\_k(g\_-g\_k)\; =\; \backslash left(-\; f\_m\; g\_m\backslash right)\; -\; \backslash sum\_^n\; g\_(f\_-\; f\_k).$ Using the forward difference operator $\backslash Delta$, it can be stated more succinctly as :$\backslash sum\_^n\; f\_k\backslash Delta\; g\_k\; =\; \backslash left(g\_\; -\; f\_m\; g\_m\backslash right)\; -\; \backslash sum\_^n\; g\_\backslash Delta\; f\_k,$ Note that summation by parts is an analogue to the integration by parts formula, :$\backslash int\; f\backslash ,dg\; =\; f\; g\; -\; \backslash int\; g\backslash ,df.$ Note also that although applications almost always deal with convergence of sequences, the statement is purely algebraic and will work in any field. It will also work when one sequence is in a vector space, and the other is in the relevant field of scalars. 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「summation by parts」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.