  Analytic formulae are presented to construct detailed secular lightcurves of
both early asymptotic giant branch (AGB) and thermally pulsing AGB stars. They
are based on an extensive grid of evolutionary calculations, performed with an
updated stellar evolution code. Basic input parameters are the initial mass
between 0.8 and 7 solar mass, metallicity of 0.0001, 0.008, 0.02, and the
mixing length theory (MLT) parameter. The formulae allow for two important
effects, namely that the first pulses do not reach the full amplitude, and hot
bottom burning (HBB) in massive stars, which are both not accounted for by core
mass - luminosity relations of the usual type.
  Furthermore, the dependence of the effective temperature and a few other
quantities characterizing the conditions at the base of the convective
envelope, which are relevant for HBB, are investigated as functions of
luminosity, total and core mass for different formulations of the convection
theory applied, MLT or Canuto & Mazzitelli's theory.
