Results 11 to 20 of about 10,363 (245)

Multivariate reciprocal differences for branched Thiele continued fraction expansions

Journal of Computational and Applied Mathematics, 1988
For a multivariate function a Viscovatov-like algorithm for the construction of a branched continued fraction expansion was developed independently by \textit{J. A Murphy} and \textit{M. R. O'Donohoe} [ibid. 4, 181-190 (1978; Zbl 0407.40002)] and by \textit{K. J. Kuchminskaya} [Dopov. Akad. Nauk Ukr. RSR, Ser.
Annie Cuyt, Brigitte Verdonk
exaly   +5 more sources

Branched continued fractions for double power series

Journal of Computational and Applied Mathematics, 1980
AbstractA branched continued fraction (BCF) is defined and some of their properties are shown. This branched continued fraction corresponds to the double power series. One theorem of Van Vleck is transformed for the case of double power series and BCF.
Siemaszko, Wojciech
exaly   +4 more sources

On convergence $(2,1,\dots,1)$-periodic branched continued fraction of the special form

Carpathian Mathematical Publications, 2015
$(2,1,\dots,1)$-periodic branched continued fraction of the special form is defined. Conditions of convergence are established for 2-periodic continued fraction and $(2,1,\dots,1)$-periodic branched continued fraction of the special form. Truncation error bounds are estimated for these fractions under additional conditions.
Bodnar, D. I., Bubniak, M. M.
openaire   +5 more sources

Positive definite branched continued fractions of special form

Carpathian Mathematical Publications, 2013
Research of the class of branched continued fractions of special form, whose denominators do not equal to zero, is proposed and the connection of such fraction with a certain quadratic form is established. It furnishes new opportunities for the investigation of convergence of branching continued fractions of special form.
R.I. Dmytryshyn, Dmytryshyn, R.I.
openaire   +4 more sources

Some properties of branched continued fractions of special form

Carpathian Mathematical Publications, 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. The uniform convergence of branched continued fraction of special form, which is a particular case of the mentioned fraction, in the some limited parabolic region is ...
R.I. Dmytryshyn, Dmytryshyn, R.I.
openaire   +4 more sources

On the convergence criterion for branched continued fractions with independent variables

Carpathian Mathematical Publications, 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. These fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series.
R.I. Dmytryshyn, Dmytryshyn, R.I.
openaire   +5 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 ...
Antonova, T.M.
openaire   +2 more sources

A Worpitzky boundary theorem for branched continued fractions of the special form

Carpathian Mathematical Publications, 2016
For a branched continued fraction of a special form we propose the limit value set for the Worpitzky-like theorem when the element set of the branched continued fraction is replaced by its boundary.
Kuchminska, Kh.Yo., Kh.Yo. Kuchminska
openaire   +6 more sources

On branched continued fraction expansions of hypergeometric functions \(F_M\) and their ratios

Modern Mathematical Methods
The paper investigates the problem of constructing branched continued fraction expansions of hypergeometric functions \(F_M(a_1,a_2,b_1,b_2;a_1,c_2;\mathbf{z})\) and their ratios. Recurrence relations of the hypergeometric function \(F_M\) are established, which provide the construction of formal branched continued fractions with simple structures, the
Ivan Nyzhnyk, Roman Dmytryshyn, Tamara Antonova   +2 more
openaire   +4 more sources

On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H4(a,b;c,d;z1,z2) Ratios

, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions by branched continued fractions. The formal branched continued fraction expansions for three different Horn’s hypergeometric function H4 ratios are ...
Roman Dmytryshyn, Tamara Antonova, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
core   +1 more source