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The bilinear generating function for products of two Laguerre 2D polynomialsLm;n(z; z0) with different arguments is calculated. It corresponds to theformula of Mehler for the generating function of products of two Hermitepolynomials. Furthermore, the generating function for mixed products ofLaguerre 2D and Hermite 2D polynomials and for products of two Hermite 2Dpolynomials is calculated. A set of infinite sums over products of two Laguerre2D polynomials as intermediate step to the generating function for products ofLaguerre 2D polynomials is evaluated but these sums possess also properimportance for calculations with Laguerre polynomials. With the technique ofSU(1; 1) operator disentanglement some operator identities are derived in anappendix. They allow to calculate convolutions of Gaussian functions combinedwith polynomials in one- and two-dimensional case and are applied to evaluatethe discussed generating functions. Keywords: Laguerre and Hermite polynomials,Laguerre 2D polynomials, Jacobi polynomials, Mehler formula, SU(1; 1) operatordisentanglement, Gaussian convolutions.

Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials