Quantum group approach to \(q\)-special functions
type: Item
instance of: scholarly article
title: Quantum group approach to \(q\)-special functions
zbMATH Open document ID: 0967.33010
DOI: 10.1023/A:1003638915593
author: R. Smith
published in: International Journal of Theoretical Physics
publication date: 2001-08-26T00:00:00Z
review text: The authors consider differential representations of a certain \(q\)-deformed \(SU(2)\) algebra and the two-dimensional quantum Euclidean algebra. The objects of their interest are the eigenfunctions of the corresponding Casimir operators, which turn out to be certain \(q\)-deformed associated Legendre polynomials in the former case and certain \(q\)-deformed Bessel functions in the latter. They succeed in finding explicit forms for their \(q\)-Bessel functions.
reviewed by: C. Krattenthaler
Mathematics Subject Classification ID: 33D80
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1529844
zbMATH Keywords: quantum algebra associated to \(SU(2)\)
zbMATH Keywords: Euclidean quantum algebra
zbMATH Keywords: Casimir operator
zbMATH Keywords: differential representation
zbMATH Keywords: \(q\)-deformed associated Legendre polynomials
zbMATH Keywords: \(q\)-Bessel functions
MaRDI profile type: Publication
full work available at URL: a:1003638915593
OpenAlex ID: W94736778
description: scientific article; zbMATH DE number 1529844