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

被引：13

作者：

Ismail, Mourad E. H. ^{[1
,2
]}

Zeng, Jiang ^{[3
]}

机构：

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[2] King Saud Univ, Riyadh, Saudi Arabia

[3] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

来源：

ADVANCES IN APPLIED MATHEMATICS | 2015年 / 64卷

关键词：

2D-Hermite polynomials; 2D-Laguerre polynomials; Kibble-Slepian formula; Linearization coefficients; Elementary symmetric functions; Inequalities; Positivity; Shifted Laguerre polynomials; LAGUERRE;

D O I：

10.1016/j.aam.2014.12.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：70 / 88

页数：19

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