%0 Journal Article
%T The Askey-Wilson function transform scheme
%A Erik Koelink
%A Jasper V. Stokman
%J Mathematics
%D 1999
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9912140v2