c transitions > We have recently presented the complete O(alpha_s^2)
corrections to the semileptonic decay width of the b quark at
maximal recoil. Here we discuss various technical aspects of that
calculation and further applications of similar methods. In
particular, we describe an expansion which facilitates the phase space
integrations and the treatment of the mixed real–virtual corrections,
for which Taylor expansion does not work and the so-called eikonal
expansion must be employed. Several terms of the
expansion are given for the O(alpha_s^2) QCD corrections
to the differential semileptonic decay width of the b –quark at
maximal recoil. We also demonstrate how the light quark loop
corrections to the top quark decay rate can be obtained using the same
methods. We briefly discuss the application of these techniques to
the calculation of the O(alpha_s^2) correction to zero
recoil sum rules for heavy flavor transitions.