On the Al-salam-Carlitz Orthogonal <i>q</i>-polynomials

Abstract

We use the q-integral representation for the Rogers-Szeg¨o polynomials to highlight a discrete measure of the Al-Salam-Carlitz form U(α q) associated with the Al-SAlam-Carlitz polynomials of the first kind {U^(α)_n (:; q)}n ≥ 0 in the positive definite case α < 0; 0 < q < 1 and a q-integral representation of the Al-SAlam-Carlitz polynomial of the second kind V^(α)_n (:; q) for α > 0; 0 < q < 1.

Quaestiones Mathematicae 35(2012), 229–234.