  We present new deep images of the Coma Cluster from the ESA Herschel Space
Observatory at wavelengths of 70, 100 and 160 microns, covering an area of 1.75
x 1.0 square degrees encompassing the core and southwest infall region. Our
data display an excess of sources at flux densities above 100 mJy compared to
blank-field surveys, as expected. We use extensive optical spectroscopy of this
region to identify cluster members and hence produce cluster luminosity
functions in all three photometric bands. We compare our results to the local
field galaxy luminosity function, and the luminosity functions from the
Herschel Virgo Cluster Survey (HeViCS). We find consistency between the shapes
of the Coma and field galaxy luminosity functions at all three wavelengths,
however we do not find the same level of agreement with that of the Virgo
Cluster.
