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

Authors:
Y. Ben Cheikh;I. Lamiri;A. Ouni
Affiliations:
Faculté des Sciences de Monastir, Département de Mathématiques, 5019 Monastir, Tunisia;ícole Supérieure des Sciences et des Technologies de Hammam Sousse, 4011 Hammam Sousse, Tunisia;Institut préparatoire aux études d'ingénieur de Monastir, 5019 Monastir, Tunisia
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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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 hypergeometricd-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.