Abstract
In this paper, we investigate the convergence of multidimensional regular С-fractions with independent variables, which are a multidimensional generalization of regular С-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. We have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional regular С-fraction with independent variables. And, in addition, 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 regular С-fraction with independent variables.
Highlights
Let N be a fixed natural number andIk = i(k) : i(k) = (i1, i2, . . . , ik), 1 ≤ ip ≤ ip−1, 1 ≤ p ≤ k, i0 = N, k ≥ 1, be the sets of multiindices
We investigate the convergence of multidimensional regular С -fractions with independent variables, which are a multidimensional generalization of regular С fractions
We have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional regular С -fraction with independent variables
Summary
Исследуется сходимость многомерных регулярных C -дробей с неравнозначными переменными, которые являются многомерным обобщением регулярных C дробей. We have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional regular С -fraction with independent variables. In addition, 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 regular С -fraction with independent variables.
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