  It has been known for some time that the entropy of hot QCD is well
reproduced by weak coupling techniques. These do not identify with perturbation
theory, known to have poor convergence properties, but involve resumming the
physics of hard thermal loops in the non-perturbative Phi-derivable two-loop
approximation. We test this approximation scheme in the limit of large flavor
number (N_f) where the exact result can be calculated for a wide range of
couplings for which the influence of the Landau pole is negligible. Using full
momentum-dependent fermionic self-energies instead of the previously only known
weighted average value to order g^3, the exact result for the entropy can be
remarkably well reproduced by the HTL resummed theory for a natural choice of
the renormalization scale, and this up to large values of the coupling. This
gives confidence in the reliability of weak coupling techniques when applied to
the thermodynamics of QCD, at least for temperatures T > 3 T_c.
