Higher QCD corrections for inclusive semileptonic B decays

In these proceedings we review the calculation of the total decay rate for inclusive $B→X_{c}ℓ \overline{ν}_{ℓ}$ decays to higher orders in perturbative QCD. The partonic rate is obtained via an asymptotic expansion around the limit $1−m_{c}/m_{b}≪1$. The same method can be used to compute kinematic moments in case no experimental cuts are applied, i.e.\ moments of the differential rate integrated over the whole phase space. We discuss the impact of the $O(α^3_{s})$ corrections on the total semileptonic decay rate
and the moments of the dilepton invariant mass $q^{2}$.