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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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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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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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Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors
Journal of High Energy Physics, 2018 By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even\ heavy quarkonium exclusive production and decays, which turns out to be the last and ...
Long-Bin Chen, Jun Jiang, Cong-Feng Qiao
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Generalized Elliptic-Type Integrals and Generating Functions
Demonstratio Mathematica, 2014 On account of analytical importance or application in certain problems in radiation physics and nuclear technology, several interesting families of elliptic-type integrals were recently studied by many authors.
Chaurasia V. B. L., Singh Yudhveer
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All orders structure and efficient computation of linearly reducible elliptic Feynman integrals
Journal of High Energy Physics, 2019 We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand, which we call the inner
Martijn Hidding, Francesco Moriello
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Semi-integration of certain algebraic expressions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one
M.I. Qureshi, J. Majid
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Calculation of integrals in MathPartner
Discrete and Continuous Models and Applied Computational Science, 2021 We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for ...
Gennadi I. Malaschonok +1 more
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Monotonicity and sharp inequalities related to complete $(p,q)$-elliptic integrals of the first kind
Comptes Rendus. Mathématique, 2020 With the aid of the monotone L’Hôpital rule, the authors verify monotonicity of some functions involving complete $(p,q)$-elliptic integrals of the first kind and the inverse of generalized hyperbolic tangent function, derive several sharp inequalities ...
Wang, Fei, Qi, Feng
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Journal of High Energy Physics, 2023 In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed
Xuhang Jiang +3 more
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