On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums
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.
Fields of Study & Subjects
Advanced Mathematical Identities
Analytic Number Theory Research
Mathematical functions and polynomials
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Document type
- Preprint