On Askey-scheme and [formula omitted]-orthogonality, I: A characterization theorem

Abstract

This is the first in a series of papers dealing with generalized hypergeometric d -orthogonal polynomials extending the polynomial families in the Askey-scheme. In this paper, we give a characterization theorem to introduce new examples of generalized hypergeometric d -orthogonal polynomials to be studied in the forthcoming works. For d = 1 , we obtain an unification of some known characterization theorems in the orthogonal polynomials theory.