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arXiv · 2601.06895

Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments

Ali Olaikhan
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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.

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Ali Olaikhan. 2026-01-11. Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments. https://arxiv.org/abs/2601.06895

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