Strong Corrections to Inclusive B to X tau nu Decays

We calculate the $\alpha_s$ corrections to the form factors which parameterize the hadronic tensor relevant for inclusive semileptonic $B \rightarrow X \tau\bar\nu_{\tau}$ and $\Lambda_b \rightarrow X \tau\bar\nu_{\tau}$ decays. We apply our results to the double differential decay rates for the decays of $B$ mesons and polarized $\Lambda_b$ baryons to polarized $\tau$ leptons, presenting them in terms of one-dimensional integrals. Formulas appropriate for insertion into a Monte-Carlo simulation are presented.