We present the near–infrared H band luminosity function ( hereafter LF ) of the Coma cluster of galaxies .
It is the deepest ever computed in the near–infrared , for any type of environment , extending over 7 magnitudes , down to \sim M _ { H } ^ { * } +6 .
The LF was computed on a near–infrared selected sample of galaxies which photometry , complete down to the typical dwarf luminosity , is presented in a companion paper .
The Coma LF can be described by a Schechter function with intermediate slope ( \alpha \sim - 1.3 ) , plus a dip at M _ { H } \sim - 22 mag .
The shape of the Coma LF in H band is quite similar to the one found in the B band and , with less confidence , to the R band LF as well .
The similarity of the LF in the optical and H bands implies that in the central region of Coma there is no new population of galaxies which is too faint to be observed in the optical band ( because dust enshrouded , for instance ) , down to the magnitudes of dwarfs .
The exponential cut of the LF at the bright end is in good agreement with the one derived from shallower near–infrared samples of galaxies , both in clusters and in the field .
This fact is suggestive of a similarity of the tip of the mass function of galaxies , irrespective of the environment where they are found .
The dip at M _ { H } \sim - 22 mag is instead unique among all the so far measured near–infrared LF , although several published observations are not deep enough or spanning a suitable wide field to distinctly detect this feature .
The faint end of the LF , reaching M _ { H } \sim - 19 mag ( roughly M _ { B } \sim - 15 ) , is steep , but less than previously suggested from shallower near–infrared observations of an adjacent region in the Coma cluster .
The differences between our measured LF and that measured previously in other regions suggests a dependency on environment of the faint end of the mass function ( below M ^ { * } +2.5 ) .