On the Al-Salam-Carlitz orthogonal q-polynomials

Abstract

We use the q-integral representation for the Rogers-Szegö polynomials to highlight a discrete measure of the Al-Salam-Carlitz form u(a, q) associated with the Al-SAlam-Carlitz polynomials of the first kind in the positive definite case a < 0, 0 < q < 1 and a q-integral representation of the Al-SAlam-Carlitz polynomial of the second kind for a > 0, 0 < q < 1.