Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Ali Olaikhan
Cited by: 0

Abstract

This paper derives closed-form expressions for four-parameter Euler sums containing generalized harmonic numbers with rational arguments, expressed in terms of the polylogarithm and Lerch transcendent, and reducible (under admissible parameter choices) to Riemann zeta and Hurwitz zeta values. It further obtains closed forms for related polylogarithmic integrals.

Fields of Study & Subjects

Advanced Mathematical Identities Analytic Number Theory Research Mathematical functions and polynomials

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 January 2026
Document type
Preprint