Quantum group approach to \(q\)-special functions (Q1585849)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Quantum group approach to \(q\)-special functions |
scientific article; zbMATH DE number 1529844
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantum group approach to \(q\)-special functions |
scientific article; zbMATH DE number 1529844 |
Statements
Quantum group approach to \(q\)-special functions (English)
0 references
26 August 2001
0 references
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.
0 references
quantum algebra associated to \(SU(2)\)
0 references
Euclidean quantum algebra
0 references
Casimir operator
0 references
differential representation
0 references
\(q\)-deformed associated Legendre polynomials
0 references
\(q\)-Bessel functions
0 references
