Simple interpolation functions for the galaxy-wide stellar initial mass
  function and its effects in early-type galaxies
  The galaxy-wide stellar initial mass function (IGIMF) of a galaxy is thought
to depend on its star formation rate (SFR). Using a catalogue of observational
properties of early-type galaxies (ETGs) and a relation that correlates the
formation timescales of ETGs with their stellar masses, the dependencies of the
IGIMF on the SFR are translated into dependencies on more intuitive parameters
like present-day luminosities in different passbands. It is found that up to a
luminosity of approximately $10^9 \ {\rm L}_{\odot}$ (quite independent of the
considered passband), the total masses of the stellar populations of ETGs are
slightly lower than expected from the canonical stellar initial mass function.
However, the actual mass of the stellar populations of the most luminous ETGs
may be up to two times higher than expected from an SSP-model with the
canonical IMF. The variation of the IGIMF with the mass of ETGs are presented
here also as convenient functions of the luminosity in various passbands.
