Results 91 to 100 of about 1,712 (185)

ELLIPTIC HYPERGEOMETRIC FUNCTIONS [PDF]

, 2008
devoted to special functions of hypergeometric type – to the plain and q-hypergeometric series and integrals. Shortly before its publication, examples of a third type of such functions, related to elliptic curves, began to appear.
V. P. Spiridonov
core  

Hadronic vacuum polarization to three loops in chiral perturbation theory

Journal of High Energy Physics
Hadronic vacuum polarization at low virtualities limits the precision of experimental tests of the standard model via important physical observables. Here we compute that effect in two-flavor chiral perturbation theory to three loops.
Laurent Lellouch, Alessandro Lupo, Mattias Sjö, Kálmán Szabo, Pierre Vanhove   +4 more
doaj   +1 more source

APPROXIMATION IN THE MEAN OF CLASSES OF FUNCTIONS WITH FRACTIONAL DERIVATIVES BY THEIR ABEL–POISSON INTEGRALS

Міжнародний науково-технічний журнал "Проблеми керування та інформатики"
The constant development of the of applied mathematics is due to its close connection with the fundamental directions of research in the related fields of natural sciences.
Т.В. Жигалло
doaj   +1 more source

The spectrum of Feynman-integral geometries at two loops

Journal of High Energy Physics
We provide a complete classification of the Feynman-integral geometries at two-loop order in four-dimensional Quantum Field Theory with standard quadratic propagators.
Piotr Bargieła, Hjalte Frellesvig, Robin Marzucca, Roger Morales, Florian Seefeld, Matthias Wilhelm, Tong-Zhi Yang   +6 more
doaj   +1 more source

Elliptic functions from hypergeometric integrals

, 2020
As a contribution to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has shown how analogues of the Jacobian elliptic functions may be derived from incomplete hypergeometric integrals in signatures three and four. We determine precisely the signatures in which the Jacobian analogues or their squares are indeed elliptic.
openaire   +2 more sources

Canonical differential equations beyond genus one

Journal of High Energy Physics
We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a ...
Claude Duhr, Franziska Porkert, Sven F. Stawinski   +2 more
doaj   +1 more source

Cubic elliptic functions [PDF]

, 2003
The function \phi(\theta;q) = ... occurs in one of Ramanujan’s inversion formulas for elliptic integrals. In this article, a common generalization of the cubic elliptic functions ... is given.
Cooper, Shaun, Shaun Cooper
core  

Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions

Journal of High Energy Physics
We present the analytic total cross section of top quark pair production in electron-positron annihilation at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD).
Long-Bin Chen, Jian Wang, Yefan Wang
doaj   +1 more source

Elliptic Integrable Systems and Special Functions

31 pages.
Hallnäs, Martin, Langmann, Edwin
openaire   +2 more sources

The Elliptic Function in Statistical Integrable Models

, 2016
We examine the group theoretical reason why various two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. The symmetry of these integrable models is SU(2) and the Boltzmann weight can be parametrized by the elliptic function in many cases.
openaire   +2 more sources