Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions
, 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 ...
Roman Dmytryshyn +2 more
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Maximising Bernoulli measures and dimension gaps for countable branched systems [PDF]
, 2020 Kifer, Peres, and Weiss proved in [A dimension gap for continued fractions with independent digits. Israel J. Math.124 (2001), 61–76] that there exists c0 > 0, such that dim μ ≤ 1-c0 for any probability measure μ, which makes the digits of the ...
Baker, Simon, Jurga, Natalia
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Representation of Some Ratios of Horn’s Hypergeometric Functions H7 by Continued Fractions
, 2023 The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Roman Dmytryshyn +3 more
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Approximation of ratio of Lauricella functions by branched continued fraction
Matematychni Studii, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bodnar, D. I., Goyenko, N. P.
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On convergence criteria for branched continued fraction
Carpathian Mathematical Publications, 2020 The starting point of the present paper is a result by E.A. Boltarovych (1989) on convergence regions, dealing with branched continued fraction \[\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^N\frac{a_{i(2)}}{1}{\atop+}\ldots{\atop+}\sum_{i_n=1}^N\frac{a_{i(n)}}{1}{\atop+}\ldots,\] where $|a_{i(2n-1)}|\le\alpha/N,$ $i_p=\overline{1,N},$ $p ...
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Lattice paths and branched continued fractions II. Multivariate Lah polynomials and Lah symmetric functions [PDF]
, 2021 We introduce the generic Lah polynomials Ln,k(ϕ), which enumerate unordered forests of increasing ordered trees with a weight ϕi for each vertex with i children.
Sokal, AD, Pétréolle, M
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, 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 $$$H_4$$$.
O.S. Bodnar +5 more
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Continued fractions with $SL(2, Z)$-branches: combinatorics and entropy
Transactions of the American Mathematical Society, 2018 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 ...
C. Carminati, ISOLA, Stefano, G. Tiozzo
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On a class of Time-fractional Continuous-state Branching Processes
, 2017 We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the classical continuous-state branching processes and Markov branching processes.
Andreis, L, Polito, F, Sacerdote, L
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Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes-Rogers and Thron-Rogers Polynomials, with Coefficientwise Hankel-Total Positivity [PDF]
, 2023 We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltjes–Rogers and Thron–Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the generating polynomials
Zhu, B-X, Sokal, AD, Pétréolle, M
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