Standard and Truncated Luminosity Functions for stars in the Gaia Era
  The luminosity function (LF) for stars is here fitted by a Schechter function
and by a Gamma probability density function. The dependence of the number of
stars on the distance, both in the low and high luminosity regions, requires
the inclusion of a lower and upper boundary in the Schechter and Gamma LFs.
Three astrophysical applications for stars are provided: deduction of the
parameters at low distances, behavior of the average absolute magnitude with
distance, and the location of the photometric maximum as a function of the
selected flux. The use of the truncated LFs allows to model the Malmquist bias.
