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 \sim 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 } -5 ~ { } log~ { } h _ { 65 } < -16 ) both at the core and outskirts of the cluster .
The R-band LF for the entire Coma cluster , fitted to Schechter form , gives ; M ^ { \ast } _ { R } = -21.79 ^ { +0.08 } _ { -0.09 } +5 ~ { } log~ { } h _ { 65 } and \alpha = -1.18 ^ { +0.04 } _ { -0.02 } .

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 .
This is remarkable given the variation in the spectral types of galaxies between field and cluster environments .
The steep faint-end slope for the LFs , observed in previous studies using photometric surveys , is not found here .
However , the LF in this study is only measured to M _ { R } = -16 , compared to much deeper limits ( M _ { R } \sim - 12 ) achieved in photometric surveys .

The total B-band LF for the Coma cluster , fitted to a Schecter form is ; M ^ { \ast } _ { B } = -19.95 ^ { +0.15 } _ { -0.10 } +5 ~ { } log~ { } h _ { 65 } and \alpha = -0.96 ^ { +0.01 } _ { -0.02 } .
This also 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 and dominates 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 .