Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

  • Johannes Broedel
  • Claude Duhr
  • Falko Dulat
  • Lorenzo Tancredi
Open Access
Regular Article - Theoretical Physics


We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.


NLO Computations QCD Phenomenology 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Johannes Broedel
    • 1
  • Claude Duhr
    • 2
    • 3
  • Falko Dulat
    • 4
  • Lorenzo Tancredi
    • 2
  1. 1.Institut für Mathematik und Institut für PhysikHumboldt-Universität zu Berlin, IRIS AdlershofBerlinGermany
  2. 2.Theoretical Physics DepartmentCERNGenevaSwitzerland
  3. 3.Center for Cosmology, Particle Physics and Phenomenology (CP3)Université Catholique de LouvainLouvain-La-NeuveBelgium
  4. 4.SLAC National Accelerator LaboratoryStanford UniversityStanfordU.S.A.

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