(q, μ) and (p, q, ζ)-exponential functions: Rogers-Szego 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-Szego 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. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3498685]