Communications in Number Theory and Physics
Volume 12 (2018)
Feynman integrals and iterated integrals of modular forms
Pages: 193 – 251
In this paper we show that certain Feynman integrals can be expressed as linear combinations of iterated integrals of modular forms to all orders in the dimensional regularisation parameter $\varepsilon$. We discuss explicitly the equal mass sunrise integral and the kite integral. For both cases we give the alphabet of letters occurring in the iterated integrals. For the sunrise integral we present a compact formula, expressing this integral to all orders in $\varepsilon$ as iterated integrals of modular forms.
Received 1 May 2017
Accepted 1 February 2018
Published 21 June 2018