Continued fractions and conformal mappings for domains with angle points

Abstract

Here we construct the conformal mappings with the help of continuous fractions approximations. These approximations converge to the algebraic roots $\sqrt[N]{z}$ for $N\in \mathbb{N}$ and $z$ from the right half-plane of the complex plane. We estimate both the convergence rate and the compact set of convergence. Also we give the examples that illustrate the introduced technique of a conformal mapping construction.