= Schwarz-Christoffel mapping
{c}
{title2=$F'(z)=C\prod_j(z-a_j)^{\alpha_j-1}$}
= Schwarz-Christoffel formula
{c}
{synonym}
A <conformal map> from the <complex upper half-plane> to a polygonal domain with finite prevertices $a_j\in\mathbb R$ and interior angles $\pi\alpha_j$ has the displayed derivative, with upper-half-plane branches of the powers. Integrating supplies the map, up to translation and nonzero scaling. For a slit boundary, repeated geometric vertices are treated as distinct boundary approaches: the two sides at the slit base have their respective angles, and a slit tip has angle $2\pi$, hence exponent one.
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