Abstract
Using an alternative definition of usual Hermite polynomials, two problems in the theory of general Hermite and Laguerre 2D polynomials can be separated with advantage for the further treatment: the introduction of a general 2D matrix in the linear transformation of powers of the components of a 2D vector and the generation of Hermite (or Laguerre) polynomials by applying an integral operator to these powers. The Jacobi polynomials appear in the finite-dimensional irreducible representations of the two-dimensional general linear group GL(2,C).
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