Some discrete d-orthogonal polynomial sets

Abstract

In this paper, we characterize all polynomial sets which are at the same time d-orthogonal and Δ ω -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.