ON SOME 2D ORTHOGONAL q-POLYNOMIALS

被引：11

作者：

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

Zhang, Ruiming ^{[1
]}

机构：

[1] Northwest A&F Univ, Coll Sci, Yangling 712100, Shaanxi, Peoples R China

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

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 10期

基金：

美国国家科学基金会;

关键词：

Disc polynomials; Zernike polynomials; 2D-Hermite polynomials; q-2D-Hermite polynomials; generating functions; ladder operators; q-Sturm-Liouville equations; q-integrals; q-Zernike polynomials; Ramanujan's beta integrals; large degree asymptotics; scaled asymptotics; connection relations; Askey-Roy integral; Rogers-Ramanujan identities; COMPLEX HERMITE-POLYNOMIALS; Q-DISK POLYNOMIALS; ADDITION FORMULA;

D O I：

10.1090/tran/6824

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues formulas for both families. We also introduce a q-2D analogue of the disk polynomials (Zernike polynomials) and derive similar formulas for them as well, including evaluating certain connection coefficients. Some of the generating functions may be related to Rogers-Ramanujan type identities.

引用

页码：6779 / 6821

页数：43

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