Some generalized hypergeometric d-orthogonal polynomial sets

In this paper, we characterize the d-orthogonal polynomial sets given by their explicit expressions in a specific basis. As application, we consider the generalized hypergeometric case to characterize d-orthogonal polynomial sets of Laguerre type, Meixner type,Meixner–Pollaczek type, Krawtchouk type, continuous dual Hahn type, and dual Hahn type. For d = 1, we obtain a unification of some characterization theorems in the orthogonal polynomials theory. © 2008 Elsevier Inc. All rights reserved.