= Initial mass function
{title2=IMF}
{wiki}
The <initial mass function> specifies the distribution of stellar <masses> at birth. Writing $\xi(M)=dN/dM$ means that $\xi(M)\,dM$ counts the expected number born in a small <mass> interval. Counts per logarithmic interval differ: $dN/d\ln M=M\xi(M)$. Confusing these conventions changes the reported slope even for the same population.
For a chosen finite birth-mass range, $\int\xi(M)\,dM$ gives the number of <stars> and $\int M\xi(M)\,dM$ their total <mass>. The <mass and luminosity weighting of a stellar initial mass function> explains why a small number of luminous massive <stars> can dominate the light without dominating the count. A present-day distribution also reflects deaths, continued <star formation>, unresolved companions and observational selection, so it is not automatically the birth distribution.
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