A refined $q$-analogue of some congruences of Van Hamme
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912364554616832 |
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| author | Wang, Chen Tian, Yu-Chan Huang, Kai |
| author_facet | Wang, Chen Tian, Yu-Chan Huang, Kai |
| contents | In 1997, Van Hamme proposed 13 supercongruences corresponding to $1/π$ series of the Ramanujan-type. Inspired by the recent work of V.J.W. Guo, we establish a unified $q$-analogue of Van Hamme's (B.2), (E.2) and (F.2) supercongruences, which is also a refinement of some known results obtained by different authors. As a consequence, we give a parametric supercongruence related to the Euler polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_04395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A refined $q$-analogue of some congruences of Van Hamme Wang, Chen Tian, Yu-Chan Huang, Kai Number Theory Combinatorics In 1997, Van Hamme proposed 13 supercongruences corresponding to $1/π$ series of the Ramanujan-type. Inspired by the recent work of V.J.W. Guo, we establish a unified $q$-analogue of Van Hamme's (B.2), (E.2) and (F.2) supercongruences, which is also a refinement of some known results obtained by different authors. As a consequence, we give a parametric supercongruence related to the Euler polynomials. |
| title | A refined $q$-analogue of some congruences of Van Hamme |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2505.04395 |