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arXiv · 1508.01816

Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials

Mourad E. H. Ismail·Ruiming Zhang
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Abstract

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

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BibTeXRIS

Mourad E. H. Ismail, Ruiming Zhang. 2015-08-01. Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials. https://arxiv.org/abs/1508.01816

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