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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 Conditional convergence ： ウィキペディア英語版 Conditional convergence In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. ==Definition== More precisely, a series $\backslash scriptstyle\backslash sum\backslash limits\_^\backslash infty\; a\_n$ is said to converge conditionally if $\backslash scriptstyle\backslash lim\backslash limits\_\backslash ,\backslash sum\backslash limits\_^m\backslash ,a\_n$ exists and is a finite number (not ∞ or −∞), but $\backslash scriptstyle\backslash sum\backslash limits\_^\backslash infty\; \backslash left|a\_n\backslash right|\; =\; \backslash infty.$ A classic example is given by :$1\; -\; +\; -\; +\; -\; \backslash cdots\; =\backslash sum\backslash limits\_^\backslash infty$ which converges to $\backslash ln\; (2)\backslash ,\backslash !$, but is not absolutely convergent (see Harmonic series). The simplest examples of conditionally convergent series (including the one above) are the alternating series. Bernhard Riemann proved that a conditionally convergent series may be rearranged to converge to any sum at all, including ∞ or −∞; see ''Riemann series theorem''. A typical conditionally convergent integral is that on the non-negative real axis of $\backslash sin\; (x^2)$ (see Fresnel integral). 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「Conditional convergence」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.