On Some 2D Orthogonal Q-Polynomials

Keywords

2D-Hermite polynomials; Askey; Connection relations; Disc polynomials; Generating functions; Ladder operators; Large degree asymptotics; Liouville equations; Q-2D-Hermite polynomials; Q-integrals; Q-Sturm; Q-Zernike polynomials; Ramanujan identities; Ramanujan’s beta integrals; Rogers; Roy integral; Scaled asymptotics; Zernike polynomials

Abstract

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.

Publication Date

1-1-2017

Publication Title

Transactions of the American Mathematical Society

Volume

369

Issue

10

Number of Pages

6779-6821

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/tran/6824

Socpus ID

85027073941 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85027073941

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