The sunrise integral and elliptic polylogarithms

2016/06/30 by Luise Adams, Adams, Luise, Christian Bogner +3 · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1606.09457

openalex publication_date 2016/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated integral structure of our functions allows us to furthermore compute the equal mass case to arbitrary order.

Citations

• Multiple polylogarithms and mixed Tate motives
• Elliptic integral evaluation of a Bessel moment by contour integration of a lattice Green function
• Multiple Elliptic Polylogarithms
• The elliptic dilogarithm for the sunset graph
• The two-loop sunrise integral around four space-time dimensions and\n generalisations of the Clausen and Glaisher functions towards the elliptic\n case

Cited by

• Feynman Fox integrals in the physical region

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