Convergence of some branched continued fractions with independent variables
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 2
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 non-zero 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 CN. And also, we have proved that a condition of convergence for the considered branched continued fractions in certain subsets of CN 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 CN, which are interior of the above mentioned subsets.
Authors and Affiliations
R. I. Dmytryshyn
Keywords
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- EP ID EP310098
- DOI 10.15330/ms.47.2.150-159
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