  We present a determination of the local (z=0) luminosity function of
optically selected type 1 (broad-line) Active Galactic Nuclei. Our primary
resource is the Hamburg/ESO Survey (HES), which provides a well-defined sample
of more than 300 optically bright AGN with redshifts z<0.3 and blue magnitudes
B<17.5. AGN luminosities were estimated in two ways, always taking care to
minimise photometric biases due to host galaxy light contamination. Firstly, we
measured broad-band B_J (blue) magnitudes of the objects over small apertures
of the size of the seeing disk. Secondly, we extracted H alpha and H beta broad
emission line luminosities from the spectra which should be entirely free of
any starlight contribution. The resulting AGN luminosity function (AGNLF) is
consistent with a single power law, also when considering the effects of number
density evolution within the narrow redshift range. We compared our AGNLF with
the H alpha luminosity function of lower luminosity Seyfert 1 galaxies by Hao
et al. (2005) and found a smooth transition between both, with excellent
agreement in the overlapping region. From the combination of HES and SDSS
samples we constructed a single local AGNLF spanning more than 4 orders of
magnitude in luminosity. It shows only mild curvature which can be well
described as a double power law with slope indices of -2.0 for the faint end
and -2.8 for the bright end. We predicted the local AGNLF in the soft X-ray
domain and compared this to recent literature data. We also compared the local
AGNLF with results obtained at higher redshifts and find strong evidence for
luminosity-dependent evolution, in the sense that AGN with luminosities around
M_B~-19 are as common in the local universe as they were at z=1.5, supporting
the 'AGN downsizing' picture (abridged).
