On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912854058205184 |
|---|---|
| author | Layja, Jorge Antonio González |
| author_facet | Layja, Jorge Antonio González |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums Layja, Jorge Antonio González Number Theory 11M32, 40C10, 11B65, 11M06 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. |
| title | On the Evaluation of Apéry-Like Series Involving Multiple $t$-Harmonic Star Sums |
| topic | Number Theory 11M32, 40C10, 11B65, 11M06 |
| url | https://arxiv.org/abs/2601.20027 |