  In the framework of the perturbative Quantum Chromodynamics factorization,
the cross section of the heavy meson production via the combination of a heavy
quark with a light one can be factorized to be the convolution of the
combination matrix element, the light quark distribution function, and the hard
partonic sub-cross section of the heavy quark production. The partonic
distribution and the combination matrix element are functions of a scaling
variable, respectively, which is the momentum fraction of the corresponding
quark with respect to the heavy meson. We studied the $D^{*\pm}$ production in
jet via combination in pp collision at the LHC. Our calculation can be summed
with the fragmentation contribution, and the total result is comparable with
the experimental data. The combination matrix elements can be further studied
in various hadron production processes.
