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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 General Dirichlet series ： ウィキペディア英語版 General Dirichlet series In the field of mathematical analysis, a general Dirichlet series is an infinite series that takes the form of : $\backslash sum\_^a\_n\; e^,$ where $a\_n$, $s$ are complex numbers and $\backslash$ is a strictly increasing sequence of positive numbers that tends to infinity. A simple observation shows that an 'ordinary' Dirichlet series : $\backslash sum\_^\backslash frac,$ is obtained by substituting $\backslash lambda\_n=\backslash log\; n$ while a power series : $\backslash sum\_^a\_n\; (e^)^n,$ is obtained when $\backslash lambda\_n=n$. == Fundamental theorems == If a Dirichlet series is convergent at $s\_0=\backslash sigma\_0+t\_0i$, then it is uniformly convergent in the domain : and convergent for any $s=\backslash sigma+ti$ where $\backslash sigma>\backslash sigma\_0$. There are now three possibilities regarding the convergence of a Dirichlet series, i.e. it may converge for all, for none or for some values of ''s''. In the latter case, there exist a $\backslash sigma\_c$ such that the series is convergent for $\backslash sigma>\backslash sigma\_c$ and divergent for . By convention, $\backslash sigma\_c=\backslash infty$ if the series converges nowhere and $\backslash sigma\_c=-\backslash infty$ if the series converges everywhere on the complex plane. 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「General Dirichlet series」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.