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

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 Padé 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.

arXiv comment31 pages, 1 table, minor corrections, references updated. To appear in Journal of the Australian Mathematical Society