Kept on Wikipedia:Schwarz function

The Schwarz function, named for Hermann Schwarz, was introduced in a 1974 book by Philip J. Davis. It defines a method by which the Schwarz reflection principle may be generalized to reflection through arbitrary analytic curves in the complex plane, not just through the real axis. Given a non-singular, analytic Jordan arc $\mathrm{\Gamma }$ in the complex plane, the Schwarz function $S$ is a uniquely determined analytic function on a neighborhood of $\mathrm{\Gamma }$ with the property that $S(z)=z^{*}$ for every point $z\in \mathrm{\Gamma }$.

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