Results 21 to 30 of about 147,754 (277)

Some convergence regions of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2013
Some circular and parabolic convergence regions for branched continued fractions of special form are established.
O.E. Baran
doaj   +8 more sources

Approximation of ratioof Lauricella functions by branched continued fraction

Matematychni Studii, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. І. Bodnar, N. P. Hoyenko
semanticscholar   +4 more sources

On structure of branched continued fractions

Carpathian Mathematical Publications
The paper provides a survey of various multidimensional generalizations of continued fractions that arose when solving the problem of approximating functions of one or several variables, including some hypergeometric functions. It is shown that all these generalizations can be considered as separate cases of the general concept of a branched continued ...
Т. М. Antonova
semanticscholar   +3 more sources

On the convergence criterion for branched continued fractions with independent variables

Karpatsʹkì Matematičnì Publìkacìï, 2018
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.
R.I. Dmytryshyn
doaj   +6 more sources

Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy [PDF]

Transactions of the American Mathematical Society, 2016
We study the dynamics of a family K_alpha of discontinuous interval maps whose (infinitely many) branches are Moebius transformations in SL(2, Z), and which arise as the critical-line case of the family of (a, b)-continued fractions. We provide an explicit construction of the bifurcation locus E_KU for this family, showing it is parametrized by Farey ...
Carlo Carminati, Stefano Isola, Giulio Tiozzo   +2 more
openalex   +4 more sources

On the numerical stability of the branched continued fraction expansion of the ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

Математичні Студії
Continued fractions and their generalization, branched continued fractions, are the effective tools used to study special functions. In this aspect, an important problem of continued fractions and branched continued fractions is the study of their ...
M. V. Dmytryshyn, C. Cesarano, O. Kondur, I.-A. Lutsiv   +3 more
doaj   +2 more sources

A truncation error bound for branched continued fractions of the special form on subsets of angular domains

Carpathian Mathematical Publications, 2023
Truncation error bounds for branched continued fractions of the special form are established. These fractions can be obtained by fixing the values of variables in branched continued fractions with independent variables, which is an effective tool for ...
D. І. Bodnar, Оксана Боднар, I.B. Bilanyk   +2 more
openalex   +3 more sources

Approximation for the Ratios of the Confluent Hypergeometric Function ${\mathbf{\Phi }}_{\mathit{D}}^{\mathbf{\left(}\mathit{N}\mathbf{\right)}}$ by the Branched Continued Fractions

Axioms, 2022
The paper deals with the problem of expansion of the ratios of the confluent hypergeometric function of N variables ΦD(N)(a,b¯;c;z¯) into the branched continued fractions (BCF) of the general form with N branches of branching and investigates the ...
Tamara Antonova, Roman Dmytryshyn, Roman Kurka   +2 more
doaj   +2 more sources

On simple circular sets of absolute convergence for branched continued fractions of the special form

Karpatsʹkì Matematičnì Publìkacìï, 2012
The radii of the circles with center in origin of coordinates that are simple sets of absolute convergence for branched continued fractions of the special form have been investigated.
T.M. Antonova
doaj   +2 more sources

Truncation Error Bounds for Branched Continued Fraction Expansions of Some Appell’s Hypergeometric Functions F2

Symmetry
This paper considers the problem of approximating some Appell’s hypergeometric functions F2 by their branched continued fraction expansions. Using the formula for the difference of two approximants of a branched continued fraction, we established the ...
Roman Dmytryshyn
openalex   +2 more sources