TY - JOUR AU - T. M. Antonova AU - R. I. Dmytryshyn PY - 2020/07/15 Y2 - 2024/03/28 TI - Truncation error bounds for branched continued fraction $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$ JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 7 SE - Research articles DO - 10.37863/umzh.v72i7.2342 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2342 AB - UDC 517.5The paper deals with the problem of estimating the error of approximation of a branched continued fraction, which is a generalization of a continued fraction. Using the method of fundamental inequalities, truncation error bounds for branched continued fraction $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots,$ whose elements belong to some rectangular sets of a complex plane, are established. The obtained results have been applied to multidimensional $S$, $A$-fraction with independent variables. ER -