Algebraicity of hypergeometric functions with arbitrary parameters

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 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.