Results 11 to 20 of about 66,566 (275)
SoftwareX, 2019 We outline a set of MATLAB functions that enable the computation of elliptic integrals and Jacobian elliptic functions for real arguments. The correctness, robustness, efficiency, and accuracy of the functions are discussed in detail.
Milan Batista
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Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism
Journal of High Energy Physics, 2018 We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have ...
Johannes Broedel +3 more
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Approximations related to the complete p-elliptic integrals
Open Mathematics, 2022 In this paper, the authors present some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, by showing the monotonicity and concavity-convexity properties of certain combinations ...
Zhong Genhong, Ma Xiaoyan, Wang Fei
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Karpatsʹkì Matematičnì Publìkacìï, 2022 In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
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Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams [PDF]
, 2017 We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the $\rho$-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in ...
Ablinger, J. +7 more
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On a procedure to derive ϵ-factorised differential equations beyond polylogarithms
Journal of High Energy Physics, 2023 In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms.
Lennard Görges +3 more
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Explicit solutions of some equations and systems of mathematical physics
Advances in Difference Equations, 2020 This paper deals at first with a fully integrable evolution system of nonlinear partial differential equations (PDEs) which is a generalization of the classical Heisenberg ferromagnet equation.
Angela Slavova, Petar Popivanov
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
Journal of High Energy Physics, 2018 We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to elliptic ...
Johannes Broedel +4 more
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Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2021 In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces.
Vasyl Kovalchuk +2 more
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Journal of High Energy Physics, 2023 We studied the two-loop non-factorizable Feynman diagrams for the t-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one internal massive ...
Zihao Wu, Ming-Ming Long
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