  We have obtained new redshifts for 265 objects in the central
48~$\times$~25~arcmin$^2$ region of the Coma cluster. When supplemented with
literature data, our redshift sample is 95~\% complete up to a magnitude
b$_{26.5}$=18.0 (the magnitudes are taken from the photometric sample of Godwin
et al. 1983). Using redshift-confirmed membership for 205 galaxies, and the
location in the colour-magnitude diagram for another 91 galaxies, we have built
a sample of cluster members which is complete up to b$_{26.5}$=20.0. We show
that the Coma cluster luminosity function cannot be adequately fitted by a
single Schechter (1976) function, because of a dip in the magnitude
distribution at b$_{26.5}$$\sim$17. The superposition of an Erlang (or a Gauss)
and a Schechter function provides a significantly better fit. We compare the
luminosity function of Coma to those of other clusters, and of the field.
Luminosity functions for rich clusters look similar, with a maximum at $M_{b}
\simeq -19.5 + 5 \times \log h_{50}$, while the Virgo and the field luminosity
functions show a nearly monotonic behaviour. These differences may be produced
by physical processes related to the environment which affect the luminosities
of a certain class of cluster galaxies.
