The kite integral to all orders in terms of elliptic polylogarithms

TL;DR

This paper demonstrates that the two-loop kite integral's Laurent series in four-dimensional space-time can be expressed using elliptic polylogarithms, providing an iterative method for computation at any order.

Contribution

It introduces a novel approach to express the kite integral in terms of elliptic polylogarithms and presents an iterative method for calculating its series expansion.

Findings

Laurent series expressed via elliptic polylogarithms

Iterative method for series expansion

Explicit first three orders provided

Abstract

We show that the Laurent series of the two-loop kite integral in $D=4-2\varepsilon$ space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations we present an iterative method to compute any desired order. As an example, we give the first three orders explicitly.