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$(q,μ)$ 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 to 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.