On the convergence of multidimensional S-fractions with independent variables

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Authors

  • O.S. Bodnar Volodymyr Gnatiuk Ternopil National Pedagogical University, 2 Kryvonosa str., 46027, Ternopil, Ukraine
  • R.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-2845-0137

DOI:

https://doi.org/10.15330/cmp.10.1.58-64

Keywords:

convergence, uniform convergence, multidimensional S-fraction with independent variables

Abstract

In this paper, we investigate the convergence of multidimensional S-fractions with independent variables, which are a multidimensional generalization of S-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. For establishing the convergence criteria, we use the convergence continuation theorem to extend the convergence, already known for a small region, to a larger region. As a result, we have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional S-fraction with independent variables. And, also, we have shown that the interior of the parabola is the domain of convergence of a branched continued fraction, which is reciprocal to the multidimensional S-fraction with independent variables. In addition, we have obtained two new convergence criteria for S-fractions as a consequences from the above mentioned results.

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Published

2018-07-03

How to Cite

(1)
Bodnar, O.; Dmytryshyn, R. On the Convergence of Multidimensional S-Fractions With Independent Variables: Array. Carpathian Math. Publ. 2018, 10, 58-64.

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Section

Scientific articles

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