  We use an expansion in angular mode functions in order to solve the Boltzmann
equation for a gluon plasma undergoing longitudinal expansion. By comparing
with the exact solution obtained numerically by other means we show that the
expansion in mode functions converges rapidly for all cases of practical
interest, and represents a substantial gain in numerical effort as compared to
more standard methods. We contrast the cases of a non expanding plasma and of
longitudinally expanding plasmas, and follow in both cases the evolutions
towards thermalization. In the latter case, we observe that, although the
spherical mode function appears to be well reproduced after some time by a
local equilibrium distribution function depending on slowly varying temperature
and chemical potential, thereby suggesting thermalization of the system, the
longitudinal and transverse pressures take more time to equilibrate. This is
because the expansion hinders the relaxation of the first angular mode
function. This feature was also observed in a simpler context where the
Boltzmann equation is solved in terms of special moments within the relaxation
time approximation, and attributed there to the particular coupling between the
first two moments of the distribution function. The present analysis confirms
this observation in a more realistic setting.
