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arXiv · 1711.04409

Continued fractions and conformal mappings for domains with angle points

Pyotr N. Ivanshin
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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.

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Pyotr N. Ivanshin. 2017-11-13. Continued fractions and conformal mappings for domains with angle points. https://arxiv.org/abs/1711.04409

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