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Wünsche, A. (2001) Hermite and Laguerre 2D Polynomials. In: Dattoli, G., Srivastava, H.M. and Cesarano, C., Eds., Advanced Special Functions and Integration Methods, Aracne Editrice, Roma, 157-198.

has been cited by the following article:

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

  AUTHORS: Alfred Wünsche

  KEYWORDS: Laguerre and Hermite Polynomials, Laguerre 2D Polynomials, Jacobi Polynomials, Mehler Formula, SU(1, 1) Operator Disentanglement, Gaussian Convolutions

  JOURNAL NAME: Applied Mathematics, Vol.6 No.12, November 30, 2015

  ABSTRACT: The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.