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  • RODRIGUES FORMULA AND LINEAR INDEPENDENCE FOR VALUES OF HYPERGEOMETRIC FUNCTIONS WITH VARYING PARAMETERS

  • MAKOTO KAWASHIMA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 117 / Issue 3 / December 2024
    Published online by Cambridge University Press:
    05 December 2023, pp. 308-344
    Print publication:
    December 2024
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  • 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.