Results 1 to 10 of about 116,820 (273)

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

Karpatsʹkì Matematičnì Publìkacìï, 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.
D.I. Bodnar, M.M. Bubniak
doaj   +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.
Ivan Nyzhnyk, Roman Dmytryshyn, Tamara Antonova   +2 more
doaj   +5 more sources

On convergence criteria for branched continued fraction

Karpatsʹkì Matematičnì Publìkacìï, 2020
The starting point of the present paper is a result by E.A. Boltarovych (1989) on convergence regions, dealing with branched continued fraction \[\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^N\frac{a_{i(2)}}{1}{\atop+}\ldots{\atop+}\sum_{i_n=1}^N\
T.M. Antonova
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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   +4 more sources

Branched continued fractions for double power series

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

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

Karpatsʹkì Matematičnì Publìkacìï, 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.
Kh.Yo. Kuchminska
doaj   +6 more sources

Positive definite branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 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.
R.I. Dmytryshyn
doaj   +4 more sources

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

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   +5 more sources

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