Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/5207
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dc.contributor.authorDmytryshyn, Roman-
dc.contributor.authorBodnar, Oksana-
dc.contributor.authorДмитришин, Роман Іванович-
dc.date.accessioned2020-04-13T18:23:55Z-
dc.date.available2020-04-13T18:23:55Z-
dc.date.issued2018-
dc.identifier.urihttp://hdl.handle.net/123456789/5207-
dc.description.abstractIn 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. 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 consequences from the above mentioned results.uk_UA
dc.language.isoenuk_UA
dc.subjectconvergenceuk_UA
dc.subjectuniform convergenceuk_UA
dc.subjectS-fractionuk_UA
dc.subjectmultidimensional S-fraction with independent variablesuk_UA
dc.titleOn the convergence of multidimensional S-fractions with independent variablesuk_UA
dc.typeArticleuk_UA
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