The $\varepsilon$-form of the differential equations for Feynman integrals in the elliptic case

Abstract

Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The $\varepsilon$-form is obtained by a (non-algebraic) change of basis for the master integrals.