Perturbative Heavy Quark Fragmentation Function through O(alpha_s^2)
  We derive the initial condition for the perturbative fragmentation function of a heavy quark through order O(alpha_s^2) in the MS-bar scheme. This initial condition is useful for computing heavy quark (or lepton, in case of QED) energy distributions from calculations with massless partons. In addition, the initial condition at O(alpha_s^2) can be used to resum collinear logarithms ln(Q^2/m^2) in heavy quark energy spectrum with next-to-next-to-leading logarithmic accuracy by solving the DGLAP equation. 
Kirill Melnikov and Alexander Mitov