  The influence of the Doppler effect in the fireball framework on the spectrum
of gamma-ray bursts is investigated. The study shows that the shape of the
expected spectrum of an expanding fireball remains almost the same as that of
the corresponding rest frame spectrum for constant radiations of the
bremsstrahlung, Comptonized, and synchrotron mechanisms as well as for that of
the GRB model. The peak flux spectrum and the peak frequency are obviously
correlated. When the value of the Lorentz factor becomes 10 times larger, the
flux of fireballs would be several orders of magnitude larger. The expansion
speed of fireballs is a fundamental factor of the enhancement of the flux of
gamma-ray bursts.
