Algebraicity of hypergeometric functions with arbitrary parameters
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929343649808384 |
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| author | Fürnsinn, Florian Yurkevich, Sergey |
| author_facet | Fürnsinn, Florian Yurkevich, Sergey |
| contents | We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and Beukers-Heckman (1989) for globally bounded and algebraic hypergeometric functions, however in a more general setting which allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12855 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraicity of hypergeometric functions with arbitrary parameters Fürnsinn, Florian Yurkevich, Sergey Classical Analysis and ODEs Combinatorics We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and Beukers-Heckman (1989) for globally bounded and algebraic hypergeometric functions, however in a more general setting which allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples. |
| title | Algebraicity of hypergeometric functions with arbitrary parameters |
| topic | Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2308.12855 |