Kibble-Slepian Formula And Generating Functions For 2D Polynomials

Keywords

2D Hermite polynomials; 2D q-Hermite polynomials; Hermite polynomials; Integral operators; Poisson kernels; Positivity of kernels

Abstract

We prove a generalization of the Kibble-Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. 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.

Publication Date

9-1-2016

Publication Title

Advances in Applied Mathematics

Volume

80

Number of Pages

70-92

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.aam.2016.05.003

Socpus ID

84973453837 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84973453837

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