Elliptic Polylogarithms and Basic Hypergeometric Functions

TL;DR

This paper explores the representation of multiple elliptic polylogarithms through integrals of basic hypergeometric functions, providing methods for their precise computation using q-difference equations.

Contribution

It introduces a novel approach to express elliptic polylogarithms as integrals of hypergeometric functions and details their computability via q-difference equations.

Findings

Elliptic polylogarithms can be represented as integrals of hypergeometric functions.

These functions are computable to arbitrary precision.

The method utilizes q-difference equations and q-contiguous relations.

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.