Algebraicity of hypergeometric functions with arbitrary parameters

Author:

Fürnsinn Florian1ORCID,Yurkevich Sergey123

Affiliation:

1. Faculty of Mathematics University of Vienna Vienna Austria

2. Team CSAI, A&R TECH GmbH Vienna Austria

3. Team MathExp Inria Saclay Île‐de‐France Palaiseau France

Abstract

AbstractWe 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 and Beukers–Heckman for globally bounded and algebraic hypergeometric functions, however, in a more general setting that allows arbitrary complex parameters with possibly integral differences. We also showcase the adapted criterion on a variety of different examples.

Funder

Austrian Science Fund

Publisher

Wiley

Reference27 articles.

1. G-Functions and Geometry

2. Siegel Normality

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5. The complete generating function for Gessel walks is algebraic

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