Some evaluation of parametric Euler sums

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:451

Article

Xu, Ce¹ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 861005, Peoples R China

关键词: Harmonic number;    Euler sum;    Riemann zeta function;    Hurwitz zeta function;   

DOI  :  10.1016/j.jmaa.2017.02.047

来源: Elsevier

【 摘 要 】

In this paper, by using the method of Contour Integral Representations and the Theorem of Residues and integral representations of series, we discuss the analytic representations of parametric Euler sums that involve harmonic numbers through zeta values and rational function series, either linearly or nonlinearly. Furthermore, we give explicit formulae for several parametric quadratic and cubic sums in terms of zeta values and rational series. Moreover, some interesting new consequences and illustrative examples are considered. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free