Tornheim-like series, harmonic numbers and zeta values

2020/08/06 by Ilham A. Aliev, Aliev, Ilham A., Ayhan Dil +1
Mathematics · #11M06 #40A25 #40B05 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2008.02488

openalex publication_date 2020/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Explicit evaluations of the Tornheim-like double series in the form ∑_n,m=1^∞ \fracH_n+m+snm( n+m+s ), s∈ \mathbbN∪ \ 0 \ and their extensions are given. Furthermore, series of the type ∑_m=1^∞ \frac2H_2m+1-H_m2m( 2m+1 ) and some other Tornheim-like multiple series are evaluated in terms of the zeta values.

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