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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 Euler summation ： ウィキペディア英語版 Euler summation In the mathematics of convergent and divergent series, Euler summation is a summability method. That is, it is a method for assigning a value to a series, different from the conventional method of taking limits of partial sums. Given a series Σ''a''''n'', if its Euler transform converges to a sum, then that sum is called the Euler sum of the original series. As well as being used to define values for divergent series, Euler summation can be used to speed the convergence of series. Euler summation can be generalized into a family of methods denoted (E, ''q''), where ''q'' ≥ 0. The (E, 0) sum is the usual (convergent) sum, while (E, 1) is the ordinary Euler sum. All of these methods are strictly weaker than Borel summation; for ''q'' > 0 they are incomparable with Abel summation. ==Definition== Euler summation is particularly used to accelerate the convergence of alternating series and allows evaluating divergent sums. :$\_\backslash ,\; \backslash sum\_^\backslash infty\; a\_j\; :=\; \backslash sum\_^\backslash infty\; \backslash frac^i\; y^\; a\_j\; .$ To justify the approach notice that for interchanged sum, Euler's summation reduces to the initial series, because :$y^\backslash sum\_^\backslash infty\; \backslash frac\}\; \}\}\; \backslash sum.$ 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「Euler summation」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.