Representation of a one class function of two variables by bicontinued fractions

M.M. Pahirya

doi:10.15421/241910

Representation of a one class function of two variables by bicontinued fractions

M.M. Pahirya (Uzhhorod National University), https://orcid.org/0000-0003-1488-3302

Abstract

Let function $$$u (z, w) = f (z) h (w)$$$ be defined on the compact set $$$\mathbf{K} \subset \mathbb{C}^2$$$. We study the problem of representation of functions of this class by the product of two continued fractions, which is called a bicontinued fraction. Some properties of Thiele reciprocal derivatives, Thiele continued fractions and regular C-fractions are proved. The possibility of representation of functions of this class by bicontinued fractions is shown. Examples are considered, domains of convergence and uniform convergence of obtained bicontinued fractions to the function are indicated.

Keywords

continued fractions; bicontinued fractions; functions of two complex variables; representation of functions

MSC 2020

30B70; 30E05; 30E10

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