Algorithms and tools for iterated Eisenstein integrals
Claude Duhr, Lorenzo Tancredi
Abstract
A bstract We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space, and to obtain fast converging series representations in each region. We illustrate our approach on the examples of hypergeometric functions that evaluate to iterated Eisenstein integrals as well as the well-known sunrise graph.
Topics & Concepts
Feynman integralIterated functionMathematicsHypergeometric functionComputationGraphEisenstein seriesSlater integralsOrder of integration (calculus)Algebra over a fieldPure mathematicsApplied mathematicsMathematical analysisAlgorithmFeynman diagramDiscrete mathematicsMathematical physicsModular formAnalytic Number Theory ResearchAdvanced Mathematical IdentitiesAdvanced Algebra and Geometry