Ali Zaghouani

Some Basic $d$-Orthogonal Polynomial Sets

Abstract:
The purpose of this paper is to study the class of polynomial sets which are at the same time $d$-orthogonal and $q$-Appell. By a linear change of variable, the resulting set reduces to $q$-Al-Salam-Carlitz polynomials, for $d=1$. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order $d+1$. We also explicitly express a $d$-dimensional functional for which the d-orthogonality holds.

Keywords:
Orthogonal polynomials, $d$-orthogonal polynomials, $d$-dimensional functional, $q$-difference operator.

MSC 2000: 42C05, 33D45