Two variable extensions of the Laguerre and disc polynomials

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This work contains a detailed study of a one parameter generalization of the 2D-Hermite polynomials and a two parameter extension of Zernike's disc polynomials. We derive linear and bilinear generating functions, and explicit formulas for our generalizations and study integrals of products of some of these 2D orthogonal polynomials. We also establish a combinatorial inequality involving elementary symmetric functions and solve the connection coefficient problem for our polynomials.