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

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
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On convergence of branched continued fraction expansions of Horn's hypergeometric function $H_3$ ratios

Karpatsʹkì Matematičnì Publìkacìï, 2021
The paper deals with the problem of convergence of the branched continued fractions with two branches of branching which are used to approximate the ratios of Horn's hypergeometric function $H_3(a,b;c;{\bf z})$. The case of real parameters $c\geq a\geq 0,
T.M. Antonova
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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
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On Some Branched Continued Fraction Expansions for Horn’s Hypergeometric Function H₄(a,b;c,d;z₁,z₂) Ratios [PDF]

Axioms, 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 constructed.
Tamara Antonova, Roman Dmytryshyn, Ilona-Anna Lutsiv, Serhii Sharyn   +3 more
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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
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Convergence criteria of branched continued fractions

Researches in Mathematics
The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
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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
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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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On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

Researches in Mathematics, 2023
The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched
R.I. Dmytryshyn, I.-A.V. Lutsiv, O.S. Bodnar   +2 more
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Generalized Hypergeometric Function ₃F₂ Ratios and Branched Continued Fraction Expansions [PDF]

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   +3 more sources