Abstract: Since the 1950s it is well-known that there is a very fruitful relation between special functions and representation theory of Lie groups by e.g. realising matrix elements of specific representations in terms of special functions. With the advent of quantum groups in the 1980s this has been generalised to special functions related to quantum groups. The case of a quantum group analogue of SU(1,1) led to some analytic difficulties and we discuss how special functions can be used to obtain a quantum group analogue of SU(1,1) in the setting of Kustermans and Vaes. The dual quantum group is related to the quantized universal enveloping algebra.