On the Proof of the Genčev-Rucki Conjecture for Multiple Apéry-Like Series
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912640494731264 |
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| author | Xu, Ce |
| author_facet | Xu, Ce |
| contents | In this paper, we employ the theories and techniques of hypergeometric functions to provide two distinct proofs of the conjectured identities involving multiple Apéry-like series with central binomial coefficients and multiple harmonic star sums, as recently proposed by Genčev and Rucki. Furthermore, we establish several more general identities for multiple Apéry-like series. Furthermore, by utilizing the method of iterated integrals, a class of multiple mixed values can be expressed as combinations of the multiple Apéry-like series identities conjectured by Genčev and Rucki and $ζ(2,\ldots,2)$, thus allowing explicit formulas for these multiple mixed values to be derived in terms of Riemann zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Proof of the Genčev-Rucki Conjecture for Multiple Apéry-Like Series Xu, Ce Number Theory In this paper, we employ the theories and techniques of hypergeometric functions to provide two distinct proofs of the conjectured identities involving multiple Apéry-like series with central binomial coefficients and multiple harmonic star sums, as recently proposed by Genčev and Rucki. Furthermore, we establish several more general identities for multiple Apéry-like series. Furthermore, by utilizing the method of iterated integrals, a class of multiple mixed values can be expressed as combinations of the multiple Apéry-like series identities conjectured by Genčev and Rucki and $ζ(2,\ldots,2)$, thus allowing explicit formulas for these multiple mixed values to be derived in terms of Riemann zeta values. |
| title | On the Proof of the Genčev-Rucki Conjecture for Multiple Apéry-Like Series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.09052 |