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arXiv · 2207.00393

Differential-Difference Properties of Hypergeometric Series

Nicolas Brisebarre·Bruno Salvy
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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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Nicolas Brisebarre, Bruno Salvy. 2022-07-01. Differential-Difference Properties of Hypergeometric Series. https://arxiv.org/abs/2207.00393

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