vix.ing · top · new · best · stats · spec

Parametric Euler Sums of Harmonic Numbers

2022/03/21 by Quan, Junjie, Wang Xiyu, Wang, Xiyu +4
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.10728

openalex publication_date 2022/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \ze(2j,2m+1) in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.

Related