TY - JOUR
AU - Bodnar, D.I.
AU - Bilanyk, I.B.
PY - 2021/11/20
Y2 - 2024/03/05
TI - Parabolic convergence regions of branched continued fractions of the special form
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 3
SE - Scientific articles
DO - 10.15330/cmp.13.3.619-630
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/5412
SP - 619-630
AB - Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established. To study the parabolic regions of convergence, the element regions and value regions technique was used. In particular, half-planes are considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form is established. The obtained results made it possible to establish the conditions for the convergence of the multidimensional $S$-fractions with independent variables.
ER -