Fourier - Gauss Transform of Bilinear Generating Functions for the Continuous q-Hermite Polynomials

Abstract

The classical Fourier-Gauss transform of bilinear generation functions for the continuous q-Hermite polynomials of Rogers are studied in detail. Our approach is essentially based on the fact that the q-Hermite functions have simple behaviour with respect to the Fourier integral transform with the q-independent exponential kernel.