Differential-Difference Properties of Hypergeometric Series

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 wellknown properties of the classical orthogonal polynomials.