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

### 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.

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*Matematychni Studii*,

*54*(1), 3-14. https://doi.org/10.30970/ms.54.1.3-14

Copyright (c) 2020 R. I. Dmytryshyn, T. M. Antonova

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Matematychni Studii is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license.