Abstract
In this paper we generalize the Schwarz—Christoffel formula for a conformal mapping of a half-plane onto a certain polygon with infinitely many vertices. We assume that the interior angles of the polygon (at unknown vertices) and the points of the real axis that are images of unknown vertices under the mentioned mapping are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].
R. B. Salimov and P. L. Shabalin, The Hilbert Boundary-Value Problem of the Theory of Analytic Functions and Its Applications (Kazansk.Matem. Ob-vo, Kazan, 2005) [in Russian].
F. D. Gakhov, Boundary-Value Problems (Nauka, Moscow, 1977) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R.B. Salimov and P.L. Shabalin, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 10, pp. 76–80.
Submitted by R.B. Salimov
About this article
Cite this article
Salimov, R.B., Shabalin, P.L. Mapping of a half-plane onto a polygon with infinitely many vertices. Russ Math. 53, 68–71 (2009). https://doi.org/10.3103/S1066369X09100107
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X09100107