Bananas of equal mass: any loop, any order in the dimensional regularisation parameter

A bstract We describe a systematic approach to cast the differential equation for the l -loop equal mass banana integral into an ε -factorised form. With the known boundary value at a specific point we obtain systematically the term of order j in the expansion in the dimensional regularisation parameter ε for any loop l . The approach is based on properties of Calabi-Yau operators, and in particular on self-duality.