This article is cited in 3 papers

A generalization of the Schwarz–Christoffel formula

R. B. Salimov, P. L. Shabalin

Kazan' State Architecture and Building University, Kazan'

Abstract: We obtain a formula for mapping the upper half-plane conformally onto a polygonal region, generalizing the Schwarz–Christoffel formula to the case of a countable set of vertices. We indicate a connection of the construction of this mapping to the solution of the Hilbert boundary value problem with a countable set of discontinuity points of the coefficients and polynomial singularity of the index.

Keywords: the Schwarz–Christoffel formula, boundary conditions, index of the problem.

UDC: 517.54

Received: 12.04.2010

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