Kibble-Slepian Formula and Generating Functions for 2D Polynomials

الأصل · EN

We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in Ism4. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.