  The time-dependent spectral profile of a resonance line in a homogeneous
expanding medium is studied by numerically solving an improved Fokker-Planck
diffusion equation. The solutions are used to determine the time required to
reach a quasi-static solution near the line center. A simple scaling law for
this relaxation time is derived and is fitted to the numerical results. The
results are applied to the case of Lyman alpha scattering during primordial
recombination of hydrogen. For a wide range of cosmological models it is found
that the relaxation times are smaller than the recombination timescale,
although not by a very large factor. Thus the standard assumption of a
quasi-static solution in cosmological recombination calculations is reasonably
valid, and should not cause substantial errors in the solutions.
