Results 41 to 50 of about 1,540,688 (355)
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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One-loop open-string integrals from differential equations: all-order α′-expansions at n points
Journal of High Energy Physics, 2020 We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings.
Carlos R. Mafra, Oliver Schlotterer
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Journal of High Energy Physics, 2021 We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves.
Simon Badger +3 more
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Legendre-type relations for generalized complete elliptic integrals [PDF]
, 2016 Legendre's relation for the complete elliptic integrals of the first and second kinds is generalized. The proof depends on an application of the generalized trigonometric functions and is alternative to the proof for Elliott's identity.
S. Takeuchi
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Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2021 In this paper, we mainly aim at highlighting the importance of (hyper-)elliptic integrals in the study of gravitational effects caused by strongly gravitating systems.
Fathi, M., Villanueva, J.R.
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On the curious series related to the elliptic integrals [PDF]
, 2016 By using the theory of the elliptic integrals, a new method of summation is proposed for a certain class of series and their derivatives involving hyperbolic functions.
S. Yakubovich
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Elliptic polylogarithms and Feynman parameter integrals [PDF]
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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A symbol and coaction for higher-loop sunrise integrals
SciPost Physics Core, 2023 We construct a symbol and coaction for the $l$-loop sunrise family of integrals, both for equal-mass and generic-mass cases. These constitute the first concrete examples of symbols and coactions for integrals involving Calabi-Yau threefolds and higher ...
Andreas Forum, Matt von Hippel
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Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means
Journal of Mathematical Analysis and Applications, 2018 Let E ( r ) be the complete elliptic integrals of the second kind and J p ( a , b ) be the one-parameter mean of two distinct positive numbers a and b defined by J p ( a , b ) = p p + 1 a p + 1 − b p + 1 a p − b p for p ≠ − 1 , 0 .
Zhen-Hang Yang
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