Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME RELATIONS ON PARAMETRIC LINEAR EULER SUMS

  • Weiguo Lu (College of Mathematics and Computer Science Tongling University) ;
  • Ce Xu (School of Mathematics and Statistics Anhui Normal University) ;
  • Jianing Zhou (School of Mathematics and Statistics Anhui Normal University)
  • Received : 2022.06.27
  • Accepted : 2022.10.11
  • Published : 2023.07.31
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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.

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Acknowledgement

The authors express their deep gratitude to Professor Jianqiang Zhao for valuable discussions and comments. The authors thank the anonymous referee for suggestions which led to improvements in the exposition. 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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