The three-loop equal-mass banana integral in ε-factorised form with meromorphic modular forms

A bstract We show that the differential equation for the three-loop equal-mass banana integral can be cast into an ε -factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. The ε -factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter ε . The alphabet of the iterated integrals contains six letters.