Truncation error bounds for branched continued fraction whose partial denominators are equal to unity

R. I. Dmytryshyn; T. M. Antonova

doi:10.30970/ms.54.1.3-14

R. I. Dmytryshyn Vasyl Stefanyk Precarpathian National University
T. M. Antonova Lviv Polytechnic National University

DOI: https://doi.org/10.30970/ms.54.1.3-14

Keywords: convergence, truncation error, branched continued fraction

Abstract

The paper deals with the problem of obtaining error bounds for branched continued fraction of the form $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$. By means of fundamental inequalities method the truncation error bounds are obtained for the above mentioned branched continued fraction providing its elements belong to some rectangular sets of
a complex plane. Applications are considered for several classes of branched continued fraction expansions including the multidimensional \emph{S}-, \emph{A}-, \emph{J}-fractions with independent variables.

Author Biographies

R. I. Dmytryshyn, Vasyl Stefanyk Precarpathian National University

Vasyl Stefanyk Precarpathian National University

Department of Mathematical and Functional Analysis

Ivano-Frankivsk, Ukraine

T. M. Antonova, Lviv Polytechnic National University

Lviv Polytechnic National University

Department of Applied Mathematics

Lviv, Ukraine

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