Mass and luminosity weighting of a stellar initial mass function ($dM/d\ln m\propto m^{2-s},dL/d\ln m\propto m^{q+1-s}$)

If birth counts obey $dN/dm\propto m^{-s}$ and individual luminosity scales as $m^q$, multiply by mass or luminosity and by $dm=md\ln m$ to obtain the displayed logarithmic weights. With $s=2.35$ and $q=4$, birth mass has weight $m^{-0.35}$ while light has weight $m^{2.65}$. Finite mass cutoffs are essential; stellar lifetimes also alter the luminosity weighting of an evolved population.