  Sari, Piran, and Narayan have derived analytic formulas to model the spectra
from gamma-ray burst blast waves that are energized by sweeping up material
from the surrounding medium. We extend these expressions to apply to general
radiative regimes and to include the effects of synchrotron self-absorption.
Electron energy losses due to the synchrotron self-Compton process are also
treated in a very approximate way. The calculated spectra are compared with
detailed numerical simulation results. We find that the spectral and temporal
breaks from the detailed numerical simulation are much smoother than the
analytic formulas imply, and that the discrepancies between the analytic and
numerical results are greatest near the breaks and endpoints of the synchrotron
spectra. The expressions are most accurate (within a factor of ~ 3) in the
optical/X-ray regime during the afterglow phase, and are more accurate when
epsilon_e, the fraction of swept-up particle energy that is transferred to the
electrons, is <~ 0.1. The analytic results provide at best order-of-magnitude
accuracy in the self-absorbed radio/infrared regime, and give poor fits to the
self-Compton spectra due to complications from Klein-Nishina effects and
photon-photon opacity.
