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. 
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     title = {Mapping of a~half-plane onto a~polygon with infinitely many vertices},
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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/

[1] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973, 736 pp. | MR

[2] Salimov R. B., Shabalin P. L., Kraevaya zadacha Gilberta teorii analiticheskikh funktsii i ee prilozheniya, Izd-vo Kazansk. matem. o-va, Kazan, 2005, 298 pp.

[3] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977, 640 pp. | MR | Zbl