Abstract:
We discuss classical Fourier-Gauss transforms of a three-parameter family of the continuous Al-Salam-Chihara polynomials p(n)(x;a,b\q). It is shown that they are related to both the continuous big q-Hermite p(n)(x;a, 0\q) and the q-Hermite p(n)(x;0, 0\q) polynomials.