Results 31 to 40 of about 1,540,688 (355)
Numerical evaluation of iterated integrals related to elliptic Feynman integrals [PDF]
Computer Physics Communications, 2020 We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand.
Moritz Walden, S. Weinzierl
semanticscholar +1 more source
Asymptotic expansion and bounds for complete elliptic integrals
, 2020 In the article, we present several new bounds for the the complete elliptic integrals K (r)= ∫ π/2 0 (1−r2 sin2 θ )−1/2dθ and E (r)= ∫ π/2 0 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1 , which are the refinements and ...
Miao-Kun Wang +3 more
semanticscholar +1 more source
On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier–Legendre expansions [PDF]
Journal of Mathematical Analysis and Applications, 2017 Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integrals, Fourier-Legendre (FL) series expansions, and ${}_p F_q$ series.
J. Campbell +2 more
semanticscholar +1 more source
The ρ parameter at three loops and elliptic integrals [PDF]
Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018), 2018 We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential ...
J. Blumlein +5 more
semanticscholar +1 more source
Semi-integration of certain algebraic expressions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one
M.I. Qureshi, J. Majid
doaj +3 more sources
Master integrals for bipartite cuts of three-loop photon self energy
Journal of High Energy Physics, 2021 We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy.
R. N. Lee, A. I. Onishchenko
doaj +1 more source
Rarefied elliptic hypergeometric functions [PDF]
, 2018 Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a special $n=1$ case,
Spiridonov, V.
core +3 more sources
Monotonicity and inequalities related to complete elliptic integrals of the second kind
, 2020 In the paper, the authors present some monotonicity properties of certain functions defined in terms of the complete elliptic integrals of the second kind and some elementary functions and, consequently, improve several known inequalities for the ...
Fei Wang +2 more
semanticscholar +1 more source
Functional Inequalities for Generalized Complete Elliptic Integrals with Two Parameters
Journal of Function Spaces, 2019 In this paper, we establish some functional inequalities for generalized complete elliptic integrals with two parameters, such as estimation of bounds and mean inequalities.
Xiangkai Dou, Li Yin, Xiu-Li Lin
doaj +1 more source
SciPost Physics Proceedings, 2022 We discuss the analytic structure of the master integrals relevant for computing the com- plete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two loops in QCD.
Ekta Chaubey
doaj +1 more source