Using our catalogue of V _ { 26.5 } isophotal magnitudes for 6756 galaxies in a region covering 60 \times 25 arcmin ^ { 2 } in the center of the Coma cluster , plus 267 galaxies in a region of 9.7 \times 9.4 arcmin ^ { 2 } around NGC 4839 , we derive the luminosity function in the magnitude range 13.5 \leq V _ { 26.5 } < 21.0 ( corresponding to the absolute magnitude range -22.24 < M _ { V 26.5 } \leq - 14.74 ) .
The luminosity function for this region is well fitted by the combination of a gaussian in its bright part and of a steep Schechter function ( of index \alpha = -1.8 ) in its faint part .
Luminosity functions derived for individual regions surrounding the brightest galaxies show less steep slopes , strongly suggesting the existence of environmental effects .
The implications of such effects and galaxy formation scenarios are discussed .