Results 11 to 20 of about 1,712 (185)
Elliptic hypergeometric functions associated with root systems [PDF]
, 2020 We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two in essence form an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integrals ...
Warnaar, Ole, +3 more
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Numerical evaluation of iterated integrals related to elliptic Feynman integrals [PDF]
, 2021 We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand.
Ballantyne, J (via Mendeley Data)
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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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Elliptic Combinatorics and Markov Processes [PDF]
, 2012 We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the case of univariate functions, and Rains in the ...
Betea, Dan Dumitru
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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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Complete elliptic integrals resulting from infinite integrals of Bessel functions [PDF]
, 1974 Infinite integrals of Bessel and modified Bessel functions reducible to complete elliptic integrals are compiled.
Okui, Shigehiko
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A functional identity involving elliptic integrals [PDF]
The Ramanujan Journal, 2017 We show that the following double integral \[\int_{0}^π{\rm d}x \int_0^x {\rm d}y \frac{1}{\sqrt{1-\smash[b]{p}\cos x}\sqrt{1+\smash[b]{q\cos y}}}\]remains invariant as one trades the parameters $p$ and $q$ for $p'=\sqrt{1-p^2}$ and $q'=\sqrt{1-q^2}$ respectively.
M. Lawrence Glasser, Yajun Zhou
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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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Nuclear Physics B, 2017 We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve.
Christian Bogner +2 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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