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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2018-09

Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi

 

Elliptic Feynman integrals and pure functions. 

 

Abstract: We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homo- geneous term. We investigate several non-trivial elliptic two-loop Feynman integrals with up to three external legs and express them in terms of our functions. We observe that in all cases they evaluate to pure combinations of elliptic multiple polylogarithms of uniform weight. This is the first time that a notion of uniform weight is observed in the context of Feynman integrals that evaluate to elliptic polylogarithms.

Keywords: Elliptic polylogarithms, Feynman integrals, pure functions.

 

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2018-09

 

 

47 pp.