Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2023; 60(4): 985-1001

Online first article March 22, 2023      Printed July 31, 2023

https://doi.org/10.4134/BKMS.b220447

Copyright © The Korean Mathematical Society.

Some relations on parametric linear Euler sums

Weiguo Lu, Ce Xu, Jianing Zhou

Tongling University; Anhui Normal University; Anhui Normal University

Abstract

Recently, Alzer and Choi [2] introduced and studied a set of the four linear Euler sums with parameters. These sums are parametric extensions of Flajolet and Salvy's four kinds of linear Euler sums [9]. In this paper, by using the method of residue computations, we will establish two explicit combined formulas involving two parametric linear Euler sums $S_{p,q}^{++}(a,b)$ and $S_{p,q}^{+-}(a,b)$ defined by Alzer and Choi, which can be expressed in terms of a linear combinations of products of trigonometric functions, digamma functions and Hurwitz zeta functions.

Keywords: Parametric linear Euler sums, contour integrations, residue computations, digamma functions, Hurwitz zeta functions

MSC numbers: Primary 11M32

Supported by: Ce Xu was supported by the National Natural Science Foundation of China (Grant No. 12101008), the Natural Science Foundation of Anhui Province (Grant No. 2108085QA01) and the University Natural Science Research Project of Anhui Province (Grant No. KJ2020A0057).

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