Context :

Aims : We investigate the Coma cluster galaxy luminosity function ( GLF ) at faint magnitudes , in particular in the u* band where basically no studies are presently available at these magnitudes , by applying photometric redshift techniques .

Methods : Cluster members were selected based on Probability Distribution Function from photometric redshift calculations applied to deep u* , B , V , R , I images covering a region of almost 1 deg ^ { 2 } ( completeness limit R \sim 24 ) .
In the area covered only by the u* image , the GLF was also derived after applying a statistical background subtraction .

Results : Global and local GLFs in the B , V , R and I bands obtained with photometric redshift selection are consistent with our previous results based on a statistical background subtraction .

The GLF in the u* band shows an increase of the faint end slope towards the outer regions of the cluster .

The analysis of the multicolor type spatial distribution reveals that late type galaxies are distributed in clumps in the cluster outskirts , where X-ray substructures are also detected and where the GLF in the u* band is steeper .

Conclusions : We can reproduce the GLFs computed with classical statistical subtraction methods by applying a photometric redshift technique .
The u* GLF slope is steeper in the cluster outskirts , varying from \alpha \sim - 1 in the cluster center to \alpha \sim - 2 in the cluster periphery .
The concentrations of faint late type galaxies in the cluster outskirts could explain these very steep slopes , assuming a short burst of star formation in these galaxies when entering the cluster .