Truncated Hypergeometric Functions and Discretized Integrals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909706615783424 |
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| author | Yamamoto, Shuji |
| author_facet | Yamamoto, Shuji |
| contents | We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between truncated series and discretized integrals which comes from the mutliple zeta values and multiple polylogarithms. We also prove the formula of Ohno-Zagier type which relates the truncated multiple polylogarithms and the truncated hypergeometric series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19793 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Truncated Hypergeometric Functions and Discretized Integrals Yamamoto, Shuji Number Theory 33C05 (Primary) 11M32 (Secondary) We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between truncated series and discretized integrals which comes from the mutliple zeta values and multiple polylogarithms. We also prove the formula of Ohno-Zagier type which relates the truncated multiple polylogarithms and the truncated hypergeometric series. |
| title | Truncated Hypergeometric Functions and Discretized Integrals |
| topic | Number Theory 33C05 (Primary) 11M32 (Secondary) |
| url | https://arxiv.org/abs/2507.19793 |