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arXiv · 2308.12855

Algebraicity of hypergeometric functions with arbitrary parameters

Florian Fürnsinn·Sergey Yurkevich
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Abstract

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.

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Florian Fürnsinn, Sergey Yurkevich. 2023-08-24. Algebraicity of hypergeometric functions with arbitrary parameters. https://arxiv.org/abs/2308.12855

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