Pressure of QCD at finite temperatures and chemical potentials

We compute the perturbative expansion of the pressure of hot QCD to order g(6)ln g in the presence of finite quark chemical potentials. In this process we evaluate all two- and three-loop vacuum diagrams of the theory at arbitrary T and mu and then use these results to analytically verify the outcome of an old order g(4) calculation of Freedman and McLerran for the zero-temperature pressure. The results for the pressure and the different quark number susceptibilities at high T are compared with recent lattice simulations showing excellent agreement especially for the chemical potential dependent part of the pressure.