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We study master integrals needed to compute the Higgs boson production crosssection via gluon fusion in the infinite top quark mass limit, using acanonical form of differential equations for master integrals, recentlyidentified by Henn, which makes their solution possible in a straightforwardalgebraic way. We apply the known criteria to derive such a suitable basis forall the phase space master integrals in afore mentioned process atnext-to-next-to-leading order in QCD and demonstrate that the method isapplicable to next-to-next-to-next-to-leading order as well by solving anon-planar topology. Furthermore, we discuss in great detail how to find anadequate basis using practical examples. Special emphasis is devoted to masterintegrals which are coupled by their differential equations.

Adequate bases of phase space master integrals for $gg \to h$ at NNLO and beyond