= Mass and luminosity weighting of a stellar initial mass function
{title2=$dM/d\ln m\propto m^{2-s},\quad dL/d\ln m\propto m^{q+1-s}$}
If birth counts obey $dN/dm\propto m^{-s}$ and individual <luminosity> scales as $m^q$, multiply by <mass> or <luminosity> and by $dm=m\,d\ln m$ 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.
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