Title
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
Copyright Status
Unknown
Socpus ID
84973453837 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84973453837
STARS Citation
Ismail, Mourad E.H. and Zhang, Ruiming, "Kibble-Slepian Formula And Generating Functions For 2D Polynomials" (2016). Scopus Export 2015-2019. 3527.
https://stars.library.ucf.edu/scopus2015/3527