2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79625In 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.17 pages, 2 figures, AMS-TeX Some formulas corrected, reference updatedClassical Analysis and ODEsQuantum Algebra33D15, 33D45 (Primary) 33D80 (Secondary)text