Evaluating Feynman integrals by differential equations

A new strategy to solve differential equations for Feynman integrals has been recently suggested. After a set of master integrals is found using the integration-by-parts method, the crucial point of this strategy is to introduce a new basis where all master integrals are pure functions of uniform transcendentality. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in epsilon in dimensional regularization. This method was successfully applied to planar three-loop four-point massless on-shell integrals, to one of two types of planar families contributing to massive two-loop Bhabha scattering in QED, to so-called K4 diagram consisting of four external vertices which are connected with each other by six lines. This method can be also applied to single-scale Feynman integrals.