Definite integrals of the complete elliptic integral K [PDF]
, 1976 Definite integrals whose integrands contain the complete elliptic integral of the first kind are ...
Glasser, M.L.
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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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On the Lp-differentiability of certain classes of functions [PDF]
, 2014 We prove the $L^p$-differentiability at almost every point for convolution products on $R^d$ of the form $K*\mu$, where $\mu$ is bounded measure and $K$ is a homogeneous kernel of degree $1-d$.
Crippa, Gianluca +7 more
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On generalized complete (p, q)-elliptic integrals [PDF]
, 2021 In this paper, we study the generalized complete (p, q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters, and establish the monotonicity, generalized convexity and concavity of ...
Göğüş, Nihat Gökhan +2 more
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Inequalities for the generalized elliptic integrals and modular functions [PDF]
, 2007 In this paper, the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions, such as ma(r) and μa(r).
Chu, Yuming, Zhang, Xiaohui, Wang, Gendi
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Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral [PDF]
, 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 mathematics and string theory.
Johannes Broedel +7 more
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Elliptic polylogarithms and Feynman parameter integrals
Journal of High Energy Physics, 2019 In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of ...
Johannes Broedel +4 more
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Mylar Balloon and Associated Geometro-Mechanical Moments
Mathematics, 2023 Starting with identifications of the very fundamental geometric characteristics of a Mylar balloon such as the profile curve, height, volume, arclength, surface area, crimping factor, etc., using the geometrical moments In(x) and In, we present explicit ...
Vasyl Kovalchuk +2 more
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A Four-Point Function for the Planar QCD Massive Corrections to Top-Antitop Production in the Gluon-Fusion Channel [PDF]
, 2019 In these proceedings we present the study of a four-point function that is involved in the evaluation of the Master Integrals necessary to compute the two-loop massive QCD planar corrections to ̄ production in the gluon fusuin channel, at hadron ...
Matteo Capozi +5 more
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A non-planar two-loop three-point function beyond multiple polylogarithms
Journal of High Energy Physics, 2017 We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for t t ¯ $$ t\overline{t} $$ production and γγ production in gluon fusion through a massive top-quark loop.
Andreas von Manteuffel, Lorenzo Tancredi
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