A curious q-analogue of Hermite polynomials

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Cigler, Johann¹  Zeng, Jiang² 

[1] Univ Vienna, Inst Math, A-1090 Vienna, Austria

[2] Univ Lyon 1, CNRS, Univ Lyon, Inst Camille Jordan,UMR 5208, F-69622 Villeurbanne, France

关键词: Hermite polynomials;    q-Hermite polynomials;    Al-Salam-Chihara polynomials;    Hankel determinants;    Catalan numbers;    Matchings;    Touchard-Riordan formula;   

DOI  :  10.1016/j.jcta.2010.09.001

来源: Elsevier

【 摘 要 】

Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials In this paper we consider a new family of q-Hermite polynomials and prove several curious properties about these polynomials One striking property is the connection with q-Fibonacci and q-Lucas polynomials The latter relation yields a generalization of the Touchard-Riordan formula (C) 2010 Elsevier Inc All rights reserved

【 授权许可】

Free