  A large spectroscopic survey is constructed of galaxies in the Coma cluster.
The survey covers a wide area (1 deg$^2$) to deep magnitudes (R ~ 19.5),
covering both the core (high density) and outskirts (intermediate to low
density) of the cluster. The spectroscopic sample consists of a total of 1191
galaxies, of which, 760 galaxies are confirmed members of the Coma cluster. A
statistical technique is developed to correct the spectroscopic sample for
incompletness. The corrected sample is then used to construct R-band luminosity
function (LF) spanning a range of 7 magnitudes (-23 < M_R < -16) both at the
core and outskirts of the cluster.
  Dependence of the LF on local environment in Coma is explored. The LFs are
found to be the same, within the errors, between the inner and outer regions
and close to those from recent measurements for field galaxies. The total
B-band LF for the Coma cluster, fitted to a Schecter form is also measured and
shows a dip at M(B) = -18 mag., in agreement with previous studies. The
implications of this feature are discussed.
  The LF is studied in B-R color intervals and shows a steep faint-end slope
for red (B-R > 1.35) galaxies, both at the core and outskirts of the cluster.
This population of low luminosity red galaxies has a higher surface density
than the blue (B-R < 1.35) star-forming population, dominating the faint-end of
the Coma cluster LF. It is found that relative number of high surface
brightness galaxies is larger at the cluster core, implying destruction of low
surface brightness galaxies in dense core environment.
