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RODRIGUES FORMULA AND LINEAR INDEPENDENCE FOR VALUES OF HYPERGEOMETRIC FUNCTIONS WITH VARYING PARAMETERS
Published online by Cambridge University Press: 05 December 2023
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.
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- Research Article
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by Michael Coons
This work is partly supported by the Research Institute for Mathematical Sciences, an international joint usage and research centre located in Kyoto University.