Quantum group approach to \(q\)-special functions
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.
\(q\)-deformed associated Legendre polynomials
scientific article; zbMATH DE number 1529844