= Linear coefficient bound for normalized univalent functions
{title2=$|a_n|\leq n(1+1/(n-1))^{n-1}\leq ne$}
For $f(z)=z+\sum_{n\geq2}a_nz^n$ in the <normalized univalent function> class, the <integral mean bound for an odd square-root transform> gives $(2\pi)^{-1}\int|f(re^{i\theta})|d\theta\leq r/(1-r)$. The <Cauchy integral formula> for <Taylor coefficients> therefore yields $|a_n|\leq r^{1-n}/(1-r)$. Choosing $r=(n-1)/n$ and applying the <logarithm tangent bound> gives the displayed bound for every $n\geq2$.
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