Comparisons between analytic and numerical calculations of GRB spectra

Formulas of Sari, Piran, and Narayan for the spectral energy distributions of gamma-ray burst blast waves are extended to include synchrotron self-absorption and Compton scattering and, given a simple numerical integration, to apply to general radiative regimes. The expressions are compared with detailed numerical simulation results and are most accurate (within a factor of similar to 3) in the optical/X-ray regime during the afterglow phase. Comparison of spectral energy distributions are made for the parameters used by Wijers and Galama to fit GRB 970508.