A $q$-analogue of Gosper's strange evaluation of the hypergeometric series
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908430153809920 |
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| author | Yamaguchi, Yuka |
| author_facet | Yamaguchi, Yuka |
| contents | In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a ${}_{2}F_{1}$-series identity with two free parameters, which was proved by Ebisu (2013), Chu (2017), and Campbell (2023) in different ways. In this paper, we present a $q$-analogue of the ${}_{2}F_{1}$-series identity, along with its generalization, by using three-term relations for the ${}_{2}ϕ_{1}$ basic hypergeometric series. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_01499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $q$-analogue of Gosper's strange evaluation of the hypergeometric series Yamaguchi, Yuka Classical Analysis and ODEs 33D15 In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a ${}_{2}F_{1}$-series identity with two free parameters, which was proved by Ebisu (2013), Chu (2017), and Campbell (2023) in different ways. In this paper, we present a $q$-analogue of the ${}_{2}F_{1}$-series identity, along with its generalization, by using three-term relations for the ${}_{2}ϕ_{1}$ basic hypergeometric series. |
| title | A $q$-analogue of Gosper's strange evaluation of the hypergeometric series |
| topic | Classical Analysis and ODEs 33D15 |
| url | https://arxiv.org/abs/2507.01499 |