Geodesic
Mapping of a~half-plane onto a~polygon with infinitely many vertices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 76-80

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In this paper we generalize the Schwarz–Christoffel formula for a conformal mapping of a half-plane onto a polygon for the case when the number of vertices of a certain polygon is infinite. We assume that the interior angles of the polygon (at unknown vertices) and points of the real axis that are images of the unknown vertices under the mentioned mapping are given.
Keywords: Schwarz–Christoffel integral, inverse problem, exponent of convergence. 
@article{IVM_2009_10_a9,
     author = {R. B. Salimov and P. L. Shabalin},
     title = {Mapping of a~half-plane onto a~polygon with infinitely many vertices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--80},
     publisher = {mathdoc},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_10_a9/}
}
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R. B. Salimov; P. L. Shabalin. Mapping of a~half-plane onto a~polygon with infinitely many vertices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2009), pp. 76-80. http://geodesic.mathdoc.fr/item/IVM_2009_10_a9/