Convergence of some branched continued fractions with independent variables 

Author 
dmytryshynr@hotmail.com
Vasyl Stefanyk Precarpathian National University, IvanoFrankivsk, Ukraine

Abstract 
In this paper, we investigate a convergence of associated
multidimensional fractions and multidimensional \emph{J}fractions
with independent variables that are closely related to each other;
the coefficients of its partial numerators are positive constants
or are nonzero complex \linebreak constants from parabolic
regions. We have established the uniform convergence of the
sequences of odd and even approximants of the above mentioned
fractions to holomorphic functions on compact subsets of certain
domains of $\mathbb{C}^N.$ And also, we have proved that a
condition of convergence for the considered branched continued
fractions in certain subsets of $\mathbb{C}^N$ is the divergence
of the series composed of its coefficients. Moreover, we have
established that the convergence is uniform to a holomorphic
function on all compact subsets of domains of $\mathbb{C}^N,$
which are interior of the above mentioned subsets.

Keywords 
convergence, uniform convergence, branched continued fraction, associated multidimensional
fraction, multidimensional Jfraction

DOI 
doi:10.15330/ms.47.2.150159

Reference 
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Pages 
150159

Volume 
47

Issue 
2

Year 
2017

Journal 
Matematychni Studii

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