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Pré-Publication, Document De Travail Année : 2023

Algebraicity of hypergeometric functions with arbitrary parameters

Résumé

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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hal-04205544 , version 1 (13-09-2023)

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Florian Fürnsinn, Sergey Yurkevich. Algebraicity of hypergeometric functions with arbitrary parameters. 2023. ⟨hal-04205544⟩
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