  We determine the luminosity function (LF) of galaxies in the core of the Coma
cluster for M_R<=-11.4 (assuming H_0=75 km/s/Mpc), a magnitude regime
previously explored only in the Local Group. Objects are counted in a deep CCD
image of Coma having RMS noise of 27.7 R mag~arcsec$^{-2}$. A correction for
objects in the foreground or background of the Coma cluster---and the
uncertainty in this correction---are determined from images of five other
high-latitude fields, carefully matched to the Coma image in both resolution
and noise level. Accurate counts of Coma cluster members are obtained as faint
as R=25.5, or M_R=-9.4. The LF for galaxies is well fit by a power law
dN/dL\propto L^\alpha, with \alpha=-1.42\pm0.05, over the range
-19.4<M_R<-11.4; faintward of this range, the galaxies are unresolved and
indistinguishable from globular clusters, but the data are consistent with an
extrapolation of the power law. Surface brightness biases are minimized since
galaxies are not subjected to morphological selection, and the limiting
detection isophote is 27.6 R mag~arcsec$^{-2}$. We find the typical
$M_R\approx-12$ Coma cluster galaxy to have an exponential scale length
$\approx200$~pc, similar to Local Group galaxies of comparable magnitude. These
extreme dwarf galaxies show a surface density increasing towards the giant
elliptical NGC~4874 as $r^{-1.3}$, similar to the diffuse light and globular
cluster distributions. The luminosity in the detected dwarf galaxies is at most
a few percent of the total diffuse light of the giant galaxies in the cluster,
and the contribution of the dwarfs to the mass of the cluster is likely
negligible as well.
