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.
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