Elfun18 – A collection of MATLAB functions for the computation of elliptic integrals and Jacobian elliptic functions of real arguments [PDF]
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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Monotonicity properties and bounds for the complete p-elliptic integrals [PDF]
Journal of Inequalities and Applications, 2018 We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Ti-Ren Huang +3 more
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Elliptic Feynman integrals and pure functions [PDF]
Journal of High Energy Physics, 2019 We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term.
Johannes Broedel +4 more
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On epsilon factorized differential equations for elliptic Feynman integrals [PDF]
Journal of High Energy Physics, 2022 In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by integrating the ...
Hjalte Frellesvig
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Third kind elliptic integrals and 1-motives [PDF]
Journal of Pure and Applied Algebra, 2019 In our PH.D. thesis we have showed that the Generalized Grothendieck's Conjecture of Periods applied to 1-motives, whose underlying semi-abelian variety is a product of elliptic curves and of tori, is equivalent to a transcendental conjecture involving ...
Bertolin, Cristiana
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Bootstrapping elliptic Feynman integrals using Schubert analysis [PDF]
Physical Review Letters, 2022 The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this Letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the
Roger Morales +4 more
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The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering [PDF]
Nuclear Physics B, 2019 We calculate the massive two–loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions.
J. Blümlein +3 more
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Approximations related to the complete p-elliptic integrals [PDF]
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 symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series [PDF]
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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Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism [PDF]
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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