  Using mid-IR and optical data, we deduce the total infrared (IR) luminosities
of galaxies in the Coma cluster and present their infrared luminosity function
(LF). The shape of the overall Coma IR LF does not show significant differences
from the IR LFs of the general field, which indicates the general independence
of global galaxy star formation on environment up to densities $\sim$ 40 times
greater than in the field (we cannot test such independence above $L_{ir}
\approx 10^{44} {\rm ergs s}^{-1}$). However, a shallower faint end slope and a
smaller $L_{ir}^{*}$ are found in the core region (where the densities are
still higher) compared to the outskirt region of the cluster, and most of the
brightest IR galaxies are found outside of the core region. The IR LF in the
NGC 4839 group region does not show any unique characteristics. By integrating
the IR LF, we find a total star formation rate in the cluster of about 97.0
$M_{\sun}{\rm yr}^{-1}$. We also studied the contributions of early- and
late-type galaxies to the IR LF. The late-type galaxies dominate the bright end
of the LF, and the early-type galaxies, although only making up a small portion
($\approx$ 15%) of the total IR emission of the cluster, contribute greatly to
the number counts of the LF at $L_{ir} < 10^{43} {\rm ergs s}^{-1}$.
