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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 Legendre chi function ： ウィキペディア英語版 Legendre chi function In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by :$$ \chi_\nu(z) = \sum_^\infty \frac. As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as :$\backslash chi\_\backslash nu(z)\; =\; \backslash frac\backslash left(-\; \backslash operatorname\_\backslash nu(-z)\backslash right).$ The Legendre chi function appears as the discrete Fourier transform, with respect to the order ν, of the Hurwitz zeta function, and also of the Euler polynomials, with the explicit relationships given in those articles. The Legendre chi function is a special case of the Lerch transcendent, and is given by :$\backslash chi\_\backslash nu(z)=2^z\backslash ,\backslash Phi\; (z^2,\backslash nu,1/2).\backslash ,$ ==Identities== :$\backslash chi\_2(x)\; +\; \backslash chi\_2(1/x)=\; \backslash frac-\backslash frac|\backslash ln\; x|\; \backslash qquad(x>0).$ :$\backslash frac\backslash chi\_2(x)\; =\; \backslash frac\; x\}.$ 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「Legendre chi function」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.