  [Abridged] The Coma cluster luminosity function (LF) from ultraviolet (2000
AA) to the near-infrared (H band) is summarized. In the UV the LF is very
steep, much steeper than in the optical. The steep Coma UV LF implies that
faint and bright galaxies give similar contributions to the total UV flux and
to the total metal production rate. The Coma UV LF is dominated by star forming
galaxies, not by massive and large galaxies. The optical Coma LF is relatively
steep (alpha=-1.4) over the 11 magnitudes sampled. We found a clear steeping of
the FL going from B to R bands, indicative of the presence of a large number of
red dwarfs, as faint as three bright globular clusters. Furthermore, using
Hubble Space Telescope images, we discover that blends of globular clusters,
not resolved in individual components due to seeing, look like dwarf galaxies
when observed from the ground and are numerous and bright. The existence of
these fake extended sources increases the steepness of the LF at faint
magnitudes, if not deal on. The near-infrared LF was computed on a
near-infrared selected sample of galaxies which photometry is complete down to
the typical dwarf (M^*+5) luminosity. The Coma LF can be described by a
Schechter function with intermediate slope (alpha~-1.3), plus a dip at M_H~-22
mag. The shape of the Coma LF in H band is quite similar to the one found in
the B band. The similarity of the LF in the optical and H bands implies that in
the central region of Coma there is no new population of galaxies which is too
faint to be observed in the optical band (because dust enshrouded, for
instance), down to the magnitudes of dwarfs.
