The relativistic corrections to the fragmentation functions for a heavy quark to $B_c$ and $B_c^{\ast }$

In this paper, we compute the relativistic corrections to the fragmentation functions (FFs) of a heavy quark to $B_c$ and $B_c^{\ast }$ within the framework of non-relativistic QCD (NRQCD) factorization. The non-singlet and singlet DGLAP evolution are also presented.