ON THE AL-SALAM-CARLITZ ORTHOGONAL q-POLYNOMIALS

We use the q-integral representation for the Rogers-Szego 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 {U-n((a)) (.; q)}(n>0) 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 V-n((a)) (.; q) for a > 0, 0 < q < 1.