On Askey-scheme and d-orthogonality, I: A characterization theorem

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. (C) 2009 Elsevier B.V. All rights reserved.