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 can not test such independence above L _ { ir } \approx 10 ^ { 44 } ~ { } { 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 } { 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 } ~ { } { ergs~ { } s } ^ { -1 } .