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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 lowdensity) of the cluster. The spectroscopic sample consists of a total of 1191galaxies, of which, 760 galaxies are confirmed members of the Coma cluster. Astatistical technique is developed to correct the spectroscopic sample forincompletness. The corrected sample is then used to construct R-band luminosityfunction (LF) spanning a range of 7 magnitudes (-23 < M_R < -16) both at thecore and outskirts of the cluster.  Dependence of the LF on local environment in Coma is explored. The LFs arefound to be the same, within the errors, between the inner and outer regionsand close to those from recent measurements for field galaxies. The totalB-band LF for the Coma cluster, fitted to a Schecter form is also measured andshows a dip at M(B) = -18 mag., in agreement with previous studies. Theimplications of this feature are discussed.  The LF is studied in B-R color intervals and shows a steep faint-end slopefor 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 densitythan the blue (B-R < 1.35) star-forming population, dominating the faint-end ofthe Coma cluster LF. It is found that relative number of high surfacebrightness galaxies is larger at the cluster core, implying destruction of lowsurface brightness galaxies in dense core environment.Comment: 42 pages, 11 Figures. Accepted for publication in Ap.

A Photometric and Spectroscopic Study of Dwarf and Giant Galaxies in the Coma Cluster. IV. The Luminosity Function