Results 11 to 20 of about 2,451 (241)
Elliptic Feynman integrals and pure functions
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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Numerical solution of two dimensional harmonic boundary problems containing singularities by conformal transformation methods [PDF]
, 1971 Numerical solutions to a class of two dimensional harmonic mixed boundary value problems defined on rectangular domains and containing singularities are obtained using conformal transformation methods.
Whiteman, J R, Papamichael, N
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Jordan's Inequality: Refinements, Generalizations, Applications and Related Problems [PDF]
, 2006 This is an expository article. Some developments on refinements, generalizations, applications of Jordan’s inequality and related problems, including some estimates for three classes of complete elliptic integrals and several proofs of Wilker’s ...
Qi, Feng
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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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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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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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Hyperelliptic Integrals to Elliptic Integrals
, 2023 International audienceConsider a hyperelliptic integral , , with . When S is of degree ≤ 4, such integral can be calculated in terms of elementary functions and elliptic integrals of three kinds .
Combot, Thierry
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Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
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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The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
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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Journal of High Energy Physics, 2023 We studied the two-loop non-factorizable Feynman diagrams for the t-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one internal massive ...
Zihao Wu, Ming-Ming Long
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