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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

MAKOTO KAWASHIMA
MAKOTO KAWASHIMA*
Affiliation:
Department of Liberal Arts and Basic Sciences, College of Industrial Engineering, Nihon University, Izumi-chou, Narashino, Chiba 275-8575, Japan
*
e-mail: [email protected]
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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 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.

Keywords

Padé approximantsRodrigues formulalinear independenceGauss hypergeometric functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , First View , pp. 1 - 37
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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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.

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