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.
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页码：70 / 88
页数：19
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