On the convergence criterion for branched continued fractions with independent variables


  • R.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0003-2845-0137


convergence, branched continued fraction with independent variables, multidimensional C-fraction with independent variables
Published online: 2018-01-02


In this paper, we consider the problem of convergence of an important type of multidimensional generalization of continued fractions, the branched continued fractions with independent variables. These fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. We have established the effective criterion of absolute convergence of branched continued fractions of the special form in the case when the partial numerators are complex numbers and partial denominators are equal to one. This result is a multidimensional analog of the Worpitzky's criterion for continued fractions. We have investigated the polycircular domain of uniform convergence for multidimensional C-fractions with independent variables in the case of nonnegative coefficients of this fraction.

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How to Cite
Dmytryshyn, R. On the Convergence Criterion for Branched Continued Fractions With Independent Variables. Carpathian Math. Publ. 2018, 9, 120-127.

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