  We present a new derivation of the O(alpha_s) angular distribution of the
outgoing $q$-quark in the production process $e^+ e^- \to\gamma,Z\to
q\,\bar{q}(g)$. In our calculation, we express the three-particle phase-space
integration of the gluon-bremsstrahlung process in terms of a general set of
analytic integral solutions. A consistent treatment of the QCD one-loop
corrections to the axial-vector current deserves special attention. This is
relevant in the derivation of the forward-backward asymmetry predicted by the
standard model. Finally, we provide the full analytical solutions for the
differential rates in closed form and conclude with numerical estimates for
bottom and top quark production.
