Differential-difference properties of hypergeometric series

Brisebarre, Nicolas; Salvy, Bruno

doi:10.1090/proc/16316

Differential-difference properties of hypergeometric series
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by Nicolas Brisebarre and Bruno Salvy;

Proc. Amer. Math. Soc. 151 (2023), 2603-2617

DOI: https://doi.org/10.1090/proc/16316

Published electronically: March 21, 2023

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Abstract:

Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product by the variable $x$. We give explicit factorizations of these equations as products of first order recurrence operators. Related recurrences are also derived for the derivative with respect to $x$. These formulas generalize well-known properties of the classical orthogonal polynomials.

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