SOME RELATIONS ON PARAMETRIC LINEAR EULER SUMS
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Recently, Alzer and Choi \cite{AC2020} 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 \cite{FS1998}. 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.
Abstract
Recently, Alzer and Choi \cite{AC2020} 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 \cite{FS1998}. 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.
참고문헌 (22)
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