Despite the great potential of the U -band galaxy luminosity function ( GLF ) to constrain the history of star formation in clusters , to clarify the question of variations of the GLF across filter bands , to provide a baseline for comparisons to high-redshift studies of the cluster GLF , and to estimate the contribution of bound systems of galaxies to the extragalactic near-UV background , determinations have so far been hampered by the generally low efficiency of detectors in the U -band and by the difficulty of constructing both deep and wide surveys .
In this paper , we present U -band GLFs of three nearby , rich clusters to a limit of M _ { U } \approx - 17.5 ( M ^ { * } _ { U } +2 ) .
Our analysis is based on a combination of separate spectroscopic and R -band and U -band photometric surveys .
For this purpose , we have developed a new maximum-likelihood algorithm for calculating the luminosity function that is particularly useful for reconstructing the galaxy distribution function in multi-dimensional spaces ( e.g. , the number of galaxies as a simultaneous function of luminosity in different filter bands , surface brightness , star formation rate , morphology , etc .
) , because it requires no prior assumptions as to the shape of the distribution function .

The composite luminosity function can be described by a Schechter function with characteristic magnitude M _ { U } ^ { * } = -19.82 \pm 0.27 and faint end slope \alpha _ { U } = -1.09 \pm 0.18 .
The total U -band GLF is slightly steeper than the R -band GLF , indicating that cluster galaxies are bluer at fainter magnitudes .
Quiescent galaxies dominate the cumulative U -band flux for M _ { U } < -14 .
The contribution of galaxies in nearby clusters to the U -band extragalactic background is < 1 \% Gyr ^ { -1 } for clusters of masses \sim 3 \times 10 ^ { 14 } to 2 \times 10 ^ { 15 } M _ { \odot } .