Deprojection of luminosity functions of galaxies in the Coma cluster

We use a simple analytic model to deproject 2-d luminosity functions (LF) of galaxies in the Coma cluster measured by Beijersbergen et al. \cite{beijersbergen_etal}. We demonstrate that the shapes of the LFs change after deprojection. It is therefore essential to correct LFs for projection effects. The deprojected LFs of the central area have best-fitting Schechter parameters of M^*_U=-18.31^+0.08_-0.08 and alpha _U=-1.27^+0.018_-0.018, M^*_B=-19.79^+0.14_-0.15 and alpha _B=-1.44^+0.016_-0.016 and M^*_r=-21.77^+0.20_-0.28 and alpha _r=-1.27^+0.012_-0.012. The corrections are not significant enough to change the previously observed trend of increasing faint end slopes with increasing distance to the cluster center. The weighted U, B, and r band slopes of the deprojected LFs show a slightly weaker steepening with increasing projected cluster radius.