Generalized Zernike or disc polynomials
type: Item
instance of: scholarly article
title: Generalized Zernike or disc polynomials
zbMATH Open document ID: 1062.33011
author: Alfred Wünsche
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: The paper is devoted to the study of the generalized Zernike or disc polynomials, which are orthogonal 2D polynomials on the unit disc and can be expressed by Jacobi polynomials of transformed arguments. Two differential equations, a first-order and a second-order one with a certain degree of freedom, and the operators of lowering and raising of the indices are derived. Finally, new generating functions are presented by using an operational representation which is alternative to the Rodrigues-type representation.
reviewed by: J. Saurer
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C80
zbMATH DE Number: 2137446
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: Laguerre 2D polynomials
zbMATH Keywords: Lie group SU(1
zbMATH Keywords: 1) and Lie algebra su(1
zbMATH Keywords: 1)
zbMATH Keywords: Recurrence relations
zbMATH Keywords: Lowering and raising operators
zbMATH Keywords: Rodrigues and operational definitions of disc polynomials
MaRDI profile type: Publication
full work available at URL: j.cam.2004.04.004
OpenAlex ID: W2025689743
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DOI: 10.1016/J.CAM.2004.04.004
description: scientific article; zbMATH DE number 2137446