Some discrete d-orthogonal polynomial sets

Authors:
Yousséf Ben Cheikh;Ali Zaghouani
Affiliations:
Faculté des Sciences de Monastir, Département de Mathématiques, 5019 Monastir, Tunisia;Institut préparatoire aux études d'ingénieurs de Gabés, Route de Medenine, 6029 Gabés, Tunisia
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

In this paper, we characterize all polynomial sets which are at the same time d-orthogonal and Δω-Appell. The resulting polynomials reduce to Charlier polynomials for (d,ω)=(1,1). Various properties of the obtained polynomials are singled out: generating function, recurrence relation of order d + 1 and a difference equation of order d + 1. We also explicitly express the d-dimensional functional for which the d-orthogonality holds.