The two-dimensional \(g\)-fraction with independent variables for double power series

DOI10.1016/j.jat.2012.09.002zbMath1270.40002OpenAlexW2061075704MaRDI QIDQ692564

R. I. Dmytryshyn

Publication date: 6 December 2012

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2012.09.002

zbMATH Keywords

convergencecontinued fractionsbranched continued fractionstwo-dimensional \(g\)-fractions with independent variables

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15)

Related Items (13)

Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$ ⋮ Lumping and reversed processes in cooperating automata ⋮ Associated branched continued fractions with two independent variables ⋮ Two-Dimensional Generalization of the Rutishauser qd -Algorithm ⋮ Some convergence regions of branched continued fractions of special form ⋮ Про нескінченні залишки гіллястого ланцюгового дробу Ньордунда для гіпергеометричних функцій Аппеля ⋮ Convergence of multidimensional \(A\)- and \(J\)-fractions with independent variables ⋮ A multidimensional generalization of the Rutishauser $qd$-algorithm ⋮ Truncation error bounds for the branched continued fraction \(\sum_{i_{1=1}}^N\frac{a_{i(1)}}{1}+\sum_{i_{2=1}}^{i_1}\frac{a_{i(2)}}{1}+\sum_{i_{3=1}}^{i_2}\frac{a_{i(3)}}{1}+\cdots \) ⋮ Truncation error bounds for branched continued fraction whose partial denominators are equal to unity ⋮ Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series ⋮ Development of the Theory of Branched Continued Fractions in 1996–2016 ⋮ Convergence and estimation of the truncation error for the corresponding two-dimensional continued fractions

Cites Work

• A review of branched continued fraction theory for the construction of multivariate rational approximants
• Branched continued fractions for double power series
• A two-variable generalization of the Stieltjes-type continued fraction
• The multidimensional generalization of \(g\)-fractions and their application.
• Univalence of Continued Fractions and Stieltjes Transforms
• The g-Algorithm
• Bounded analytic functions in the unit disk and the behaviour of certain analytic continued fractions near singular line.
• Continued Fractions and Totally Monotone Sequences
• On the convergence of multidimensional \(g\)-fraction
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