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arXiv · 2305.19616

Rodrigues formula and linear independence for values of hypergeometric functions with parameters vary

Makoto Kawashima
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Abstract

In this article, we prove a generalized Rodrigues formula for a wide class of holonomic Laurent series, which yields a new linear independence criterion concerning their values at algebraic points. This generalization yields a new construction of Pad\'e approximations including those for Gauss hypergeometric functions. In particular, we obtain a linear independence criterion over a number field concerning values of Gauss hypergeometric functions, allowing the parameters of Gauss hypergeometric functions to vary.

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Makoto Kawashima. 2023-05-31. Rodrigues formula and linear independence for values of hypergeometric functions with parameters vary. https://arxiv.org/abs/2305.19616

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