We present the K -band local luminosity function derived froma sample of 1056 bright ( K < 15 ) K -selected galaxies from the Hawaii-AAO K -band redshift survey .
The Hawaii-AAO K -band redshift survey covers 4 equatorial fields with a total area of 8.22 \hbox { deg } ^ { 2 } .
We derive both the non-parametric and Schechter luminosity function from our data , and determine M ^ { * } ( K ) = -23.70 \pm 0.08 + 5 \log _ { 10 } ( h ) , \alpha = -1.37 \pm 0.10 and \phi ^ { * } = 0.013 \pm 0.003 ~ { } h ^ { 3 } ~ { } \hbox { Mpc } ^ { -3 } for a universe with \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0.7 .
We also measure the K -band luminosity function for the early- and later-type galaxies from our morphologically classified subsample .
It appears that later-type galaxies have a fainter M ^ { * } and a steep slope , while early-type galaxies have a much brighter M ^ { * } and a quite flat slope in their K -band luminosity functions .
This is consistent with what have been found in optical type dependent luminosity function .
The K -band luminosity density derived using our luminosity function is now measured at a similar redshift depth to optical luminosity densities in the SDSS redshift survey .
It is 2 times higher than the previous measurement from the shallower 2MASS sample and resolves the previously reported discrepancies between optical and near-IR luminosity densities .