Solution regularity and co-normal derivatives for elliptic systems with non-smooth coefficients on Lipschitz domains [PDF]
, 2013 This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 ElsevierElliptic PDE systems of the second order with coefficients from L∞ or Holder-Lipschitz spaces are considered in ...
Mikhailov, SE
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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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Three-loop contributions to the ρ parameter and iterated integrals of modular forms
Journal of High Energy Physics, 2020 We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model.
Samuel Abreu +3 more
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Three improvements in reduction and computation of elliptic integrals [PDF]
, 2002 Three improvements in reduction and computation of elliptic integrals are made. 1. Reduction formulas, used to express many elliptic integrals in terms of a few standard integrals, are simplified by modifying the definition of intermediate "basic ...
Carlson, B.C.
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On-shell Z boson production at hadron colliders through 𝒪(αα s )
Journal of High Energy Physics, 2022 The analytical expressions of the mixed QCD-EW corrections to on-shell Z boson inclusive production cross section at hadron colliders are presented, together with computational details.
Roberto Bonciani +3 more
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Efficient evaluation of incomplete elliptic integrals and functions [PDF]
, 1988 The impetus for this work came as a result of finding that evaluation of the complete elliptic integrals using theta-function expansions was computationally faster, for the same accuracy, than the well known conventional method using Landen's ...
Lemczyk, T.F., Yovanovich, M.M.
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Elliptic modular graph forms. Part I. Identities and generating series
Journal of High Energy Physics, 2021 Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker-Eisenstein series. The simplest
Eric D’Hoker +2 more
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Elliptic polylogarithms and two-loop Feynman integrals [PDF]
, 2018 We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are closely related to ...
Brenda Penante +9 more
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Bounds for symmetric elliptic integrals [PDF]
, 2003 Lower and upper bounds for the four standard incomplete symmetric elliptic integrals are obtained. The bounding functions are expressed in terms of the elementary transcendental functions.
Neuman, Edward
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An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
Journal of High Energy Physics, 2023 In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward.
Christoph Dlapa +2 more
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