e-mail: natig@aluxe.matcuer.unam.mx

**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.