  We use more than 110500 galaxies from the 2dF galaxy redshift survey (2dFGRS)
to estimate the b_J-band galaxy luminosity function at redshift z=0, taking
account of evolution, the distribution of magnitude measurement errors and
small corrections for incompletenessin the galaxy catalogue. Throughout the
interval -16.5>M- 5log h>-22, the luminosity function is accurately described
by a Schechter function with M* -5log h =-19.66+/-0.07, alpha=-1.21+/-0.03 and
phistar=(1.61+/-0.08) 10^{-2} h^3/Mpc^3, giving an integrated luminosity
density of rho_L=(1.82+/-0.17) 10^8 h L_sol/Mpc^3 (assuming an Omega_0=0.3,
Lambda_0=0.7 cosmology). The quoted errors have contributions from the accuracy
of the photometric zeropoint, large scale structure in the galaxy distribution
and, importantly, from the uncertainty in the appropriate evolutionary
corrections. Our luminosity function is in excellent agreement with, but has
much smaller statistical errors than an estimate from the Sloan Digital Sky
Survey (SDSS) data when the SDSS data are accurately translated to the b_J-band
and the luminosity functions are normalized in the same way. We use the
luminosity function, along with maps describing the redshift completeness of
the current 2dFGRS catalogue, and its weak dependence on apparent magnitude, to
define a complete description of the 2dFGRS selection function. Details and
tests of the calibration of the 2dFGRS photometric parent catalogue are also
presented.
