Results 11 to 20 of about 1,540,688 (355)
Generalized Elliptic Integrals [PDF]
Computational Methods and Function Theory, 2008 32 pages, 4 ...
Heikkala, Ville +2 more
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Modular transformations of elliptic Feynman integrals [PDF]
Nuclear Physics B, 2021 We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast numerical ...
Stefan Weinzierl
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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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Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral [PDF]
Physical Review D, 2017 We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure math- ematics and string theory.
Broedel, Johannes +3 more
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Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams [PDF]
Journal of Mathematics and Physics, 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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Hertz theory and Carlson elliptic integrals
Journal of the mechanics and physics of solids, 2018 Legendre's well-known elliptic integrals are not the only version of elliptic integrals. Carlson's form, developed in the late 1970s, have many advantages, and are particularly well suited for Hertzian contact analysis.
J. A. Greenwood
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All orders structure and efficient computation of linearly reducible elliptic Feynman integrals [PDF]
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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Monotonicity properties and bounds involving the complete elliptic integrals of the first kind [PDF]
, 2018 In the article, we establish several monotonicity properties of the functions involving the complete elliptic integral of the first kind. As applications, we present sharp bounds for the complete elliptic integral of the first kind and the arithmetic ...
Zhen-Hang Yang +2 more
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The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms [PDF]
Physical Review Letters, 2018 We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation for the ...
Bourjaily, Jacob L. +4 more
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