Elliptic Polylogarithms and Basic Hypergeometric Functions

Abstract

Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.

14 pages, 3 figures

References in corpus (5)

• The kite integral to all orders in terms of elliptic polylogarithms
• The iterated structure of the all-order result for the two-loop sunrise integral
• The sunrise integral and elliptic polylogarithms
• Nonterminating Basic Hypergeometric Series and the $q$-Zeilberger Algorithm
• On convergence of basic hypergeometric series

Cited by in corpus (35)

• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• Elliptic Feynman integrals and pure functions
• The $\epsilon$-form of the differential equations for Feynman integrals in the elliptic case
• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• An Elliptic Generalization of Multiple Polylogarithms
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• The unequal mass sunrise integral expressed through iterated integrals on ${\overline{\mathcal{M}}}_{1,3}$
• Elliptic polylogarithms and Feynman parameter integrals
• Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral
• An analytic solution for the equal-mass banana graph
• Maximal Cuts in Arbitrary Dimension
• Numerical evaluation of iterated integrals related to elliptic Feynman integrals
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• Numerical Loop-Tree Duality: contour deformation and subtraction
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• The electron self-energy in QED at two loops revisited
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• The complete set of two-loop master integrals for Higgs + jet production in QCD
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• Modular transformations of elliptic Feynman integrals
• Iterated integrals over letters induced by quadratic forms
• Cuts and Isogenies
• Manifestly Causal Loop-Tree Duality
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• Sunrise integral with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms
• Electroweak double-box integrals for Moller scattering
• Differential equations for Feynman integrals beyond multiple polylogarithms
• From elliptic curves to Feynman integrals
• A Feynman integral depending on two elliptic curves
• Scalar one-loop 4-point integral with one massless vertex in loop regularization