q-analogues of the G.2 Supercongruence of Van Hamme
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929502363320320 |
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| author | Liu, Yudong Wang, Xiaoxia |
| author_facet | Liu, Yudong Wang, Xiaoxia |
| contents | Motivated by the recent research of congruences and $q$-congruences, we provide two different $q$-analogues of the (G.2) supercongruence of Van Hamme through the `creative microscoping' method, which was devised by Guo and Zudilin. It is a remarkable fact that this is the first time to give direct $q$-analogues of (G.2). In addition, we propose a conjecture related to Swisher's Dwork-type supercongruence (G.3). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_01417 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | q-analogues of the G.2 Supercongruence of Van Hamme Liu, Yudong Wang, Xiaoxia Number Theory Combinatorics Motivated by the recent research of congruences and $q$-congruences, we provide two different $q$-analogues of the (G.2) supercongruence of Van Hamme through the `creative microscoping' method, which was devised by Guo and Zudilin. It is a remarkable fact that this is the first time to give direct $q$-analogues of (G.2). In addition, we propose a conjecture related to Swisher's Dwork-type supercongruence (G.3). |
| title | q-analogues of the G.2 Supercongruence of Van Hamme |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2008.01417 |