FOURIER EXPANSIONS AND INTEGRAL REPRESENTATIONS FOR THE APOSTOL-BERNOULLI AND APOSTOL-EULER POLYNOMIALS

被引：62

作者：

Luo, Qiu-Ming ^{[1
,2
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[2] Jiaozuo Univ, Dept Math, Jiaozuo 454003, Henan, Peoples R China

来源：

MATHEMATICS OF COMPUTATION | 2009年 / 78卷 / 268期

关键词：

Lipschitz summation formula; Fourier expansion; integral representation; Apostol-Bernoulli and Apostol-Euler polynomials and numbers; Bernoulli and Euler polynomials and numbers; Hurwitz Zeta function; Lerch's functional equation; rational arguments; RATIONAL ARGUMENTS; FORMULAS; ORDER;

D O I：

10.1090/S0025-5718-09-02230-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known results.

引用

页码：2193 / 2208

页数：16

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