We analyze the Luminosity Functions (LFs) of a subsample of 69 clusters from the RASS-SDSS galaxy cluster catalog. The cluster LFs are computed within the physical sizes of the galaxy systems, $r_{500}$ and $r_{200}$. When calculated within the cluster physical sizes, all the cluster LFs appear to have the same shape, well fitted by a composite of two Schechter functions with a marked upturn and a steepening at the faint-end.

We determine the composite LF for early- and late-type galaxies, where the typing is based on the galaxy $u-r$ colors. The late-type LF is well fitted by a single Schechter function with a steep slope. The early-type LF instead cannot be fitted by a single Schechter function, and a composite of two Schechter functions is needed. The faint-end upturn of the global cluster LF is due to the early-type cluster galaxies. The shape of the bright-end tail of the early-type LF does not seem to depend upon the local galaxy density or the distance from the cluster center. The late-type LF shows a significant variation only very near the cluster center. On the other hand, the faint-end tail of the early-type LF shows a significant and continuous variation with the environment.