English

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

Classical Analysis and ODEs 2016-05-10 v2

Abstract

We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the 22D Hermite polynomials recently proved in \cite{Ism4}. We derive integral representations for the 22D Hermite polynomials which are of independent interest. Several new generating functions for 22D qq-Hermite polynomials will also be given.

Keywords

Cite

@article{arxiv.1508.01816,
  title  = {Kibble-Slepian Formula and Generating Functions for 2$D$ Polynomials},
  author = {Mourad E. H. Ismail and Ruiming Zhang},
  journal= {arXiv preprint arXiv:1508.01816},
  year   = {2016}
}

Comments

26 pages

R2 v1 2026-06-22T10:28:53.950Z