On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums

Jorge Antonio González Layja

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arXiv · 2601.20027

On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums

Jorge Antonio González Layja

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Abstract

We evaluate, by elementary means, a new family of Apéry-like series involving multiple $t$-harmonic star sums of even weight. Using trigonometric expansions, inverse tangent integrals, and binomial recurrences, we obtain explicit closed-form evaluations of these series as finite alternating sums of products of Dirichlet beta values. Several explicit examples are derived as corollaries.

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Jorge Antonio González Layja. 2026-01-27. On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums. https://arxiv.org/abs/2601.20027

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