Elliptic Polylogarithms and Basic Hypergeometric Functions

2016/10/18 by Giampiero Passarino · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP

paper · pdf · doi:10.1140/epjc/s10052-017-4623-1

14 pages, 3 figures

arxiv created 2016/10/18 · arxiv updated 2017/04/05

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.

Cited by

• The q-extension of iterated integrals and nested sums in quantum field theory

Related

• Representation of solutions of the Gauss hypergeometric equation by the multiple polylogarithms, functional relations of the multiple polylogarithms and relations of the multiple zeta values
• Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values
• Harmonic Polylogarithms
• Elliptic polylogarithms and two-loop Feynman integrals
• Duality of one-variable multiple polylogarithms and their q-analogues