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Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H₃ Ratios

Mathematics, 2021
The paper deals with the problem of construction and investigation of branched continued fraction expansions of special functions of several variables. We give some recurrence relations of Horn hypergeometric functions H3. By these relations the branched
Tamara Antonova, Roman Dmytryshyn, Victoriia Kravtsiv   +2 more
doaj   +2 more sources

Truncation error bounds for branched continued fraction whose partial denominators are equal to unity

Математичні Студії, 2020
The paper deals with the problem of obtaining error bounds for branched continued fraction of the form $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$.
R. I. Dmytryshyn, T. M. Antonova
doaj   +2 more sources

Generalized Hypergeometric Function ₃F₂ Ratios and Branched Continued Fraction Expansions

Axioms, 2021
The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional ...
Tamara Antonova, Roman Dmytryshyn, Serhii Sharyn   +2 more
doaj   +2 more sources

Continued fraction expansions for complex numbers - a general approach [PDF]

, 2015
We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a
Dani, S. G.
core   +2 more sources

On some symmetric multidimensional continued fraction algorithms [PDF]

Ergodic Theory and Dynamical Systems, 2015
We compute explicitly the density of the invariant measure for the Reverse algorithm which is absolutely continuous with respect to Lebesgue measure, using a method proposed by Arnoux and Nogueira. We also apply the same method on the unsorted version of
Arnoux, Brentjes, Kraaikamp, PIERRE ARNOUX, Schweiger, SÉBASTIEN LABBÉ   +5 more
core   +6 more sources

Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2007
We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained.
Luc Vinet, Alexei Zhedanov
doaj   +5 more sources

Continued fractions

Quadratic Number Theory, 2019
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.
Álvaro González Hernández
semanticscholar   +3 more sources

On numerical stability of continued fractions

Математичні Студії
The paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun, V. Кravtsiv, M. Dmytryshyn, R. Rusyn   +3 more
doaj   +2 more sources

A note on the length of some finite continued fractions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, based on a 2008 result of Lasjaunias, we compute the lengths of simple continued fractions for some rational numbers whose numerators and denominators are explicitly given.
Khalil Ayadi, Chiheb Ben Bechir
doaj   +1 more source

Parabolic convergence regions of branched continued fractions of the special form

Karpatsʹkì Matematičnì Publìkacìï, 2021
Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established.
D.I. Bodnar, I.B. Bilanyk
doaj   +1 more source