Univalent conformal mappings onto polygonal domains with countable set of vertices by generalized Christoffel–Schwarz integral

Abstract

© 2017, Allerton Press, Inc.We propose a formula for the conformalmapping of the upper half-plane onto a polygonal domain, which generalizes the Schwarz–Christoffel equation. It is obtained by terms of partial solution to the Hilbert boundary-value problem with a countable set of singularity points of the coefficients including a turbulence of logarithmic type at the infinity point. We also prove the existence of closed and univalent mappings.