(q,μ) and (p,q,ζ)-exponential functions: Rogers–Szegő polynomials and Fourier–Gauss transform

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers–Szegő polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier–Gauss transform of a generalization of the deformed exponential functions.