Development of the Theory of Branched Continued Fractions in 1996–2016

DOI10.1007/s10958-018-3828-7zbMath1399.40008OpenAlexW2800991382MaRDI QIDQ4642281

Kh. Yo. Kuchmins'ka, D. I. Bodnar

Publication date: 22 May 2018

Published in: Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3828-7

zbMATH Keywords

matrix continued fractiondomain of convergence for branching fractions

Mathematics Subject Classification ID

Convergence and divergence of series and sequences of functions (40A30) Convergence and divergence of continued fractions (40A15)

Related Items (1)

Representation of a quotient of solutions of a four-term linear recurrence relation in the form of a branched continued fraction

Cites Work

• Boundary versions of the Worpitzky theorem for two-dimensional continued fractions
• Associated branched continued fractions with two independent variables
• The two-dimensional \(g\)-fraction with independent variables for double power series
• On the stability to perturbations of branching continued fractions with complex elements.
• Continued fractions. Vol. 1: Convergence theory
• Branched continued fractions for double power series
• A two-variable generalization of the Stieltjes-type continued fraction
• Some properties of two-dimensional continued fractions
• On sufficient conditions for convergence of two-dimensional continued fractions
• Approximation of ratio of Lauricella functions by branching continued fraction.
• Truncation error bounds for two-dimensional continued \(g\)-fraction.
• A Criterion of Convergence of a Branched Continued Fraction with Positive Elements
• Sufficient Conditions for the Equivalent Convergence of Sequences of Different Approximants for Two-Dimensional Continued Fractions
• Stability in the Calculation of Two-Dimensional Continued Fractions
• Estimates of the Rate of Pointwise and Uniform Convergence for One-Periodic Branched Continued Fractions of a Special Form
• Some convergence regions of branched continued fractions of special form
• Оцінки швидкості збіжності 1-періодичного гіллястого ланцюгового дробу спеціального вигляду
• A Worpitzky boundary theorem for branched continued fractions of the special form
• Properties of reciprocal derivatives
• On convergence $(2,1,\dots,1)$-periodic branched continued fraction of the special form
• Interpolational Integral Continued Fractions
• On the convergence of multidimensional \(g\)-fraction
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