The kite integral to all orders in terms of elliptic polylogarithms

Abstract

We show that the Laurent series of the two-loop kite integral in $D=4-2\epsilon$ 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.

19 pages, v2: version to be published

References in corpus (8)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Lectures on differential equations for Feynman integrals
• Feynman Diagrams and Differential Equations
• Resolution of singularities for multi-loop integrals
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The massless higher-loop two-point function
• Elliptic integral evaluations of Bessel moments
• A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

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