Perturbative heavy quark fragmentation function through O(αs2):: Gluon initiated contribution -: art. no. 054021

We derive the gluon initiated contribution to the initial condition for the perturbative fragmentation function of a heavy quark through order O(alpha(2)(s)) in the (MS) over bar scheme. This result is needed for the resummation with next-to-next-to-leading logarithmic accuracy of quasicollinear logarithms ln(k)(m(2)) in heavy quark differential distributions by solving the complete Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation. Together with the previously evaluated fermion initiated components, this result completes the derivation of the initial condition for the perturbative. fragmentation function at next-to-next-to-leading order.