  From R-band images of 39 Hickson compact groups (HCGs), we use galaxy counts
to determine a luminosity function extending to M_R=-14.0, approximately two
magnitudes deeper than previous compact group luminosity functions. We find
that a single Schechter function is a poor fit to the data, so we fit a
composite function consisting of separate Schechter functions for the bright
and faint galaxies. The bright end is best fit with M^*=-21.6 and alpha=-0.52
and the faint end with M^*=-16.1 and alpha=-1.17. The decreasing bright end
slope implies a deficit of intermediate luminosity galaxies in our sample of
HCGs and the faint end slope is slightly steeper than that reported for earlier
HCG luminosity functions. Furthermore, luminosity functions of subsets of our
sample reveal more substantial dwarf populations for groups with x-ray halos,
groups with tidal dwarf candidates, and groups with a dominant elliptical or
lenticular galaxy. Collectively, these results support the hypothesis that
within compact groups, the initial dwarf galaxy population is replenished by
"subsequent generations" formed in the tidal debris of giant galaxy
interactions.
