Title

A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials

Authors

Authors

M. E. H. Ismail;J. Zeng

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Adv. Appl. Math.

Keywords

2D-Hermite polynomials; 2D-Laguerre polynomials; Kibble-Slepian formula; Linearization coefficients; Elementary symmetric functions; Inequalities; Positivity; Shifted Laguerre polynomials; HERMITE-POLYNOMIALS; Mathematics, Applied

Abstract

The first author has recently proved a Kibble-Slepian type formula for the 2D-Hermite polynomials {H-m,H- n(z, (z) over bar)} which extends the Poisson kernel for these polynomials. We provide a combinatorial proof of a closely related formula. The combinatorial structures involved are the so-called m-involutionary l-graphs. They are enumerated in two different manners: first globally, then as the exponential of their connected components. We also give a combinatorial model for the 2D-Laguerre polynomials and study their linearization coefficients. (C) 2014 Elsevier Inc. All rights reserved.

Journal Title

Advances in Applied Mathematics

Volume

64

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

70

Last Page

88

WOS Identifier

WOS:000348883400005

ISSN

0196-8858

Share

COinS