TY - JOUR
AU - Dmytryshyn, R. I.
AU - Antonova, T. M.
PY - 2020/10/05
Y2 - 2021/12/09
TI - Truncation error bounds for branched continued fraction whose partial denominators are equal to unity
JF - Matematychni Studii
JA - Mat. Stud.
VL - 54
IS - 1
SE - Articles
DO - 10.30970/ms.54.1.3-14
UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/37
SP - 3-14
AB - 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 ofa 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.
ER -