Parametric Euler Sums of Harmonic Numbers
Number Theory
2022-03-22 v1
Abstract
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions, linear and quadratic parametric Euler sums. Furthermore, we also give an explicit evaluation of alternating double zeta values in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.
Cite
@article{arxiv.2203.10728,
title = {Parametric Euler Sums of Harmonic Numbers},
author = {Junjie Quan and Xiyu Wang and Xiaoxue Wei and Ce Xu},
journal= {arXiv preprint arXiv:2203.10728},
year = {2022}
}