The Askey-Wilson function transform scheme
Classical Analysis and ODEs
2007-05-23 v2 Quantum Algebra
Abstract
In this paper we present an addition to Askey's scheme of q-hypergeometric orthogonal polynomials involving classes of q-special functions which do not consist of polynomials only. The special functions are q-analogues of the Jacobi and Bessel function, and are Askey-Wilson functions, big q-Jacobi functions and little q-Jacobi functions and the corrresponding q-Bessel functions. The generalised orthogonality relations and the second order q-difference equations for these families are given. Limit transitions between these families are discussed. The quantum group theoretic interpretations are discussed shortly.
Cite
@article{arxiv.math/9912140,
title = {The Askey-Wilson function transform scheme},
author = {Erik Koelink and Jasper V. Stokman},
journal= {arXiv preprint arXiv:math/9912140},
year = {2007}
}
Comments
17 pages, 2 figures, AMS-TeX Some formulas corrected, reference updated