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Article
Computer Science, Artificial Intelligence
J. Bluemlein et al.
Summary: This article focuses on the precision calculations in perturbative Quantum Chromodynamics (QCD). It introduces new symbolic tools to enhance the computer understanding of QCD. The article discusses the emergence of hypergeometric structures in single and multiscale Feynman integrals and proposes methods to solve the associated (partial) differential equations.
ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
(2023)
Article
Mathematics, Applied
I. B. Bilanyk et al.
Summary: In this study, we introduce the concept of C-figure convergence for branched continued fractions of a special form and use it to generalize the Thron-Jones theorem on the parabolic domains of convergence of continued fractions. We propose a new method for investigating the parabolic domains of convergence of branched continued fractions, which does not rely on the Stieltjes-Vitali theorem. By proving the theorem, we make use of the stability property of continued fractions under perturbations established in this work.
UKRAINIAN MATHEMATICAL JOURNAL
(2023)
Article
Mathematics, Applied
Tamara Antonova et al.
Summary: This paper deals with the representation problem of Horn's hypergeometric functions using branched continued fractions. The formal branched continued fraction expansions for three different Horn's hypergeometric function H-4 ratios are constructed. A two-dimensional generalization of the classical method of constructing Gaussian continued fractions is employed. It is proven that the branched continued fraction converges uniformly to a holomorphic function of two variables on every compact subset of some domain H, H subset of C-2, and that this function is an analytic continuation of this ratio in the domain H. The application to the approximation of functions of two variables associated with Horn's double hypergeometric series H-4 is considered, and the expression of solutions of some systems of partial differential equations is indicated.
Article
Mathematics, Applied
R. I. Dmytryshyn
Summary: The paper focuses on the convergence problem of special classes of branched continued fractions, including multidimensional A- and J-fractions with independent variables which are extensions of A-fractions and J-fractions, respectively. By extending known convergence results from a small domain to a larger domain, new convergence criteria have been established for these branched continued fractions.
COMPUTATIONAL METHODS AND FUNCTION THEORY
(2022)
Article
D. І. Bodnar et al.
Journal of Mathematical Sciences
(2022)
Article
Mathematics, Applied
Tamara Antonova et al.
Summary: This paper deals with the expansion problem of confluent hypergeometric function ratios and describes it using branched continued fractions. The convergence of these fractions and their analytical continuation in the complex domain are investigated.
Article
Mathematics, Interdisciplinary Applications
Minjie Luo et al.
Summary: In this paper, we investigate Saran's hypergeometric function F-K and establish two related Erdelyi-type integrals. These integrals have applications in specific branches of applied physics and statistics and generalize previous research findings.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Min-Jie Luo et al.
Summary: Motivated by recent applications in physics and statistics, this study further investigates Saran's work on the hypergeometric function FK. The analytic continuation and asymptotics of FK are obtained through a new single contour integral representation, and a new integral identity is proved using fractional integration by parts. Various special cases and their relationship with Koschmieder's work are discussed in detail.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Tamara Antonova et al.
Summary: This paper discusses the construction and investigation of branched continued fraction expansions of special functions of several variables, particularly focusing on the Horn hypergeometric function H-3. Recurrence relations are provided for H-3, leading to the construction of branched continued fraction expansions for H-3 ratios. Convergence criteria are established for these fractions in both real and complex domains, with proof of convergence to the functions' analytic continuations in certain domains and consideration of applications to systems of partial differential equations.
Article
Mathematics
D. Bodnar et al.
Summary: Effective criteria of convergence for branched continued fractions of special form with positive elements were established using the criterion of convergence. The study of parabolic regions of convergence utilized the technique of element regions and value regions, with half-planes considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form was established, providing conditions for the convergence of multidimensional S-fractions with independent variables.
CARPATHIAN MATHEMATICAL PUBLICATIONS
(2021)
Article
Mathematics
R. Dmytryshyn et al.
Summary: The paper discusses the approximation of functions of several variables by branched continued fractions. It explores the correspondence between formal multiple power series and multidimensional S-fractions with independent variables, and establishes the necessary and sufficient conditions for such expansions. Numerical experiments demonstrate the efficiency and feasibility of using branched continued fractions to approximate functions of several variables from their formal multiple power series.
CARPATHIAN MATHEMATICAL PUBLICATIONS
(2021)
Article
Physics, Particles & Fields
Barak Kol et al.
JOURNAL OF HIGH ENERGY PHYSICS
(2019)
