We report an analytic expression for the dielectric function ε of GaN as a continuous function of energy from 0.74 to 6.42 eV and of temperature from 26 to 690 K. The ε spectra on which the analysis is based were obtained by using rotating-compensator spectroscopic ellipsometry. The dielectric function parametric model (DFPM) was used to provide the representation because it could accommodate the asymmetric nature of the features of the critical point. The GaN data could be successfully represented with three DFPM components and a pole and yielded ε as a continuous function of both energy and temperature over the ranges given above. Our results should be useful in a number of contexts, including device design and in-situ monitoring of GaN deposition.