A left and right truncated Schechter luminosity function for quasars
  The luminosity function for quasars (QSOs) is usually fitted by a Schechter
function. The dependence of the number of quasars on the redshift, both in the
low and high luminosity regions, requires the inclusion of a lower and upper
boundary in the Schechter function. The normalization of the truncated
Schechter function is forced to be the same as that for the Schechter function,
and an analytical form for the average value is derived. Three astrophysical
applications for QSOs are provided: deduction of the parameters at low
redshifts, behavior of the average absolute magnitude at high redshifts, and
the location (in redshift) of the photometric maximum as a function of the
selected apparent magnitude. The truncated Schechter function with the double
power law and an improved Schechter function are compared as luminosity
functions for QSOs. The chosen cosmological framework is that of the flat
cosmology, for which we provided the luminosity distance, the inverse relation
for the luminosity distance, and the distance modulus.
