  Luminosity functions and their integrated luminosity densities are presented
for the 6dF Galaxy Survey (6dFGS). This ongoing survey ultimately aims to
measure around 150,000 redshifts and 15,000 peculiar velocities over almost the
entire southern sky at |b|>10 deg. The main target samples are taken from the
2MASS Extended Source Catalog and the SuperCOSMOS Sky Survey catalogue, and
comprise 138,226 galaxies complete to (K, H, J, rF, bJ) = (12.75, 13.00, 13.75,
15.60, 16.75). These samples are comparable in size to the optically-selected
Sloan Digital Sky Survey and 2dF Galaxy Redshift Survey samples, and improve on
recent near-infrared-selected redshift surveys by more than an order of
magnitude in both number and sky coverage. The partial samples used in this
paper contain a little over half of the total sample in each band and are ~90
percent complete.
  Luminosity distributions are derived using the 1/Vmax, STY and SWML
estimators, and probe 1 to 2 absolute magnitudes fainter in the near-infrared
than previous surveys. The effects of magnitude errors, redshift incompleteness
and peculiar velocities have been taken into account and corrected throughout.
Generally, the 6dFGS luminosity functions are in excellent agreement with those
of similarly-sized surveys. Our data are of sufficient quality to demonstrate
that a Schechter function is not an ideal fit to the true luminosity
distribution, due to its inability to simultaneously match the faint end slope
and rapid bright end decline. Integrated luminosity densities from the 6dFGS
are consistent with an old stellar population and moderately declining star
formation rate.
