  Analytical calculation is presented of the QCD radiative corrections to the
rate of the process $b\to c\tau\bar\nu_\tau$ and to the $\tau$ lepton
longitudinal polarization in $\tau\bar\nu_\tau$ rest frame. The results are
given in the form of one dimensional infrared finite integrals over the
invariant mass of the leptons. We argue that this form may be optimal for
phenomelogical applications due to a possible breakdown of semilocal
hadron-parton duality in decays of heavy flavours.
