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]. 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.