Majorant series
= Majorant series
{title2=$f\ll g$}
A power series $g(x)=\sum_\alpha b_\alpha x^\alpha$ with nonnegative coefficients majorizes $f(x)=\sum_\alpha a_\alpha x^\alpha$ when $|a_\alpha|\leq b_\alpha$ for every <multi-index> $\alpha$. Coefficientwise majorization turns estimates for an analytic equation into estimates for a simpler positive-coefficient equation.