Associated branched continued fractions with two independent variables

DOI10.1007/s11253-015-1011-6zbMath1349.30011OpenAlexW2076495644MaRDI QIDQ317558

R. I. Dmytryshyn

Publication date: 4 October 2016

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-015-1011-6

zbMATH Keywords

approximantbranched continued fractionsformal double power series

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15)

Related Items (9)

Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$ ⋮ 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 ⋮ Multidimensional associated fractions with independent variables and multiple power series ⋮ Convergence and estimation of the truncation error for the corresponding two-dimensional continued fractions

Cites Work

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• The two-dimensional \(g\)-fraction with independent variables for double power series
• A review of branched continued fraction theory for the construction of multivariate rational approximants
• Branched continued fractions for double power series
• Corresponding branched continued functions with linear partial numerators for a double power series
• Continued fractions with applications
• A two-variable generalization of the Stieltjes-type continued fraction
• The multidimensional generalization of \(g\)-fractions and their application.

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