Results 21 to 30 of about 160,837 (188)

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

Karpatsʹkì Matematičnì Publìkacìï, 2019
The quotient of two linearly independent solutions of a four-term linear recurrence relation is represented in the form of a branched continued fraction with two branches of branching by analogous with continued fractions.
I.B. Bilanyk, D.I. Bodnar, L. Buyak
doaj   +2 more sources

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   +3 more sources

On the branched continued fraction expansions of the complete group of ratios of the generalized hypergeometric function $_4F_3$

Researches in Mathematics
The paper considers the classical problem of the rational approximation of analytic functions of complex variable, in particulary, to issues that arise when constructing branched continued fraction expansions for generalized hypergeometric functions ...
Y. Lutsiv, T. Antonova, R. Dmytryshyn, M. Dmytryshyn   +3 more
doaj   +2 more sources

Branched continued fraction representations of ratios of Horn's confluent function $\mathrm{H}_6$

Constructive Mathematical Analysis, 2023
In this paper, we derive some branched continued fraction representations for the ratios of the Horn's confluent function $\mathrm{H}_6.$ The method employed is a two-dimensional generalization of the classical method of constructing of Gaussian ...
T. Antonova, R. Dmytryshyn, S. Sharyn
semanticscholar   +3 more sources

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   +6 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 priori bounds for truncation error of branched continued fraction expansions of Horn's hypergeometric functions $H_4$ and their ratios

Researches in Mathematics
The paper considers the extension of analytic functions by a special family of functions — branched continued fractions. The truncation error bounds for branched continue fraction expansions of the Horn's hypergeometric functions $H_4$ and their ratios ...
R.I. Dmytryshyn, C. Cesarano, M. Dmytryshyn, I.-A.V. Lutsiv   +3 more
doaj   +2 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
T. Antonova
semanticscholar   +2 more sources

Some properties of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2015
The fact that the values of the approximates of the positive definite branched continued fraction of special form are all in a certain circle is established for the certain conditions.
R.I. Dmytryshyn
doaj   +3 more sources

Continuants algorithm for evaluation approximants of branched continued fraction

Physico-Mathematical Modelling and Informational Technologies, 2023
O. Manziy, V. Hladun, Viktor Seredynskyi
semanticscholar   +2 more sources