This article is cited in 5 papers

Brief communications

Mapping of a half-plane onto a polygon with infinitely many vertices

R. B. Salimov, P. L. Shabalin

Chair of Higher Mathematics, Kazan State Architecture and Building University, Kazan, Russia

Abstract: 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.

UDC: 517.54

Received: 17.02.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:10, 68–71

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