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

Abstract

Let function u(z, w) = f(z)h(w) be defined on the comp. 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.