= Differentiability estimate for a mapping-out function
{title2=$|g_K(z)-z-\operatorname{hcap}(K)/(z-\xi)|\le Cr\operatorname{hcap}(K)/|z-\xi|^2$}
If a <compact H-hull> lies in a disc of radius $r$ centred at $\xi\in\mathbb R$, the displayed estimate holds for $|z-\xi|>2r$, with an absolute constant $C$. It refines the Laurent expansion uniformly in the hull and supplies the first-order increment needed to derive the <Chordal Loewner equation> from the <Loewner local growth property>.
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