TY - JOUR
AU - T. M. Antonova
AU - R. I. Dmytryshyn
PY - 2020/07/15
Y2 - 2024/07/24
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 - Ukrainsâ€™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 -