  Fragmentation is the dominant production mechanism for heavy hadronic bound
states with large transverse momentum. We numerically calculate the initial
$g\rightarrow H(Q\bar{Q})$ fragmentation functions (FFs) using the
nonrelativistic QCD factorization approach. Our analytical expression of FFs
depends on both the momentum fraction $z$ and the transverse momentum of the
gluon, and contains most of the kinematical and dynamical properties of the
process. Specifically, using the perturbative QCD we present the FF for a gluon
to split into $S$-wave charmonium meson $H_c$ to leading order in the QCD
coupling constant.
