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.
Highlights
There is a wide class of Feynman integrals, mainly related to massless theories, which can be expressed in terms of multiple polylogarithms
More challenging are Feynman integrals, which cannot be expressed in terms of multiple polylogarithms
Work supported by the Research Executive Agency (REA) of the European Union under the Grant Agreement PITN-GA-2012-316704 (HiggsTools)
Summary
There is a wide class of Feynman integrals, mainly related to massless theories, which can be expressed in terms of multiple polylogarithms. More challenging are Feynman integrals, which cannot be expressed in terms of multiple polylogarithms. Evaluating this integrals one encounters elliptic generalizations of (multiple) polylogarithms (EP); examples can be found in Refs. From a more abstract point of view on (multiple) elliptic polylogarithms, in particular on their analytic structure, see Refs. [6,7] and Refs. An interesting problem is to find a suitable integral representation and the analytic continuation of EPs and an efficient algorithm for their numerical evaluation
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