  Analytic formulae are given for order alpha_s perturbative QCD corrections to
the double differential distribution of the tau lepton energy and the invariant
mass of the tau + antineutrino system in semileptonic decays of the bottom
quark. The corresponding distribution for B meson decays are obtained by
combining these results and the nonperturbative QCD corrections calculated by
Falk et al. The moments of the energy distribution of the tau lepton are
calculated.
