On some 2D orthogonal q-polynomials

2014/11/18 by Mourad E. H. Ismail, Ismail, Mourad E. H., Ruiming Zhang +1
Chemistry · Mathematics · #33C45 #33C50 #33D45 #33D50 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.1411.5223

openalex publication_date 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Zernike polynomials and atmospheric turbulence*

Related

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• Some generating functions for q-polynomials
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• A curious q-analogue of Hermite polynomials
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