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Report number	arXiv:1712.07089 ; CERN-TH-2017-273 ; CP3-17-57 ; HU-EP-17-29 ; HU-Mathematik-2017-09 ; SLAC-PUB-17194 ; CERN-TH-2017-273
Title	Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
Author(s)	Broedel, Johannes (Humboldt U., Berlin, Inst. Math. ; Humboldt U., Berlin) ; Duhr, Claude (CERN ; Louvain U., CP3) ; Dulat, Falko (SLAC) ; Tancredi, Lorenzo (CERN)
Publication	2018-05-15
Imprint	2017-12-19
Number of pages	54
Note	55 pages
In:	JHEP 05 (2018) 093
DOI	10.1007/JHEP05(2018)093
Subject category	Particle Physics - Phenomenology ; Particle Physics - Theory ; hep-ph ; hep-th
Abstract	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.
Copyright/License	arXiv nonexclusive-distrib. 1.0 publication: (License: CC-BY-4.0)

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