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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 List of mathematical series ： ウィキペディア英語版 List of mathematical series This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. *Here, $0^0$ is taken to have the value $1$ *$B\_n(x)$ is a Bernoulli polynomial. *$B\_n$ is a Bernoulli number, and here, $B\_1=-\backslash frac.$ *$E\_n$ is an Euler number. *$\backslash zeta(s)$ is the Riemann zeta function. *$\backslash Gamma(z)$ is the gamma function. *$\backslash psi\_n(z)$ is a polygamma function. *$\backslash operatorname\_s(z)$ is a polylogarithm. ==Sums of powers== See Faulhaber's formula. *$\backslash sum\_^m\; k^=\backslash frac\backslash ,\backslash !$ The first few values are: *$\backslash sum\_^m\; k=\backslash frac\backslash ,\backslash !$ *$\backslash sum\_^m\; k^2=\backslash frac=\backslash frac+\backslash frac+\backslash frac\backslash ,\backslash !$ *$\backslash sum\_^m\; k^3$ =\left()^2=\frac+\frac+\frac\,\! See zeta constants. *$\backslash zeta(2n)=\backslash sum^\_\; \backslash frac\; \backslash frac\}$ The first few values are: *$\backslash zeta(2)=\backslash sum^\_\; \backslash frac=\backslash frac\backslash ,\backslash !$ (the Basel problem) *$\backslash zeta(4)=\backslash sum^\_\; \backslash frac=\backslash frac\backslash ,\backslash !$ *$\backslash zeta(6)=\backslash sum^\_\; \backslash frac=\backslash frac\backslash ,\backslash !$ 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「List of mathematical 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.