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The initial phase of the inspiral process of a binary system producing gravitational waves can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph contributes. We consider the case where the two objects making up the binary system have equal masses. We express all master integrals related to the equal-mass H-graph up to weight four in terms of multiple polylogarithms. We provide a numerical program which evaluates all master integrals up to weight four in the physical regions with arbitrary precision.

We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all other correlation functions may be expressed.

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

We show that a recently discovered relation, which expresses tree-level single trace Einstein–Yang–Mills amplitudes with one graviton and (n−1) gauge bosons as a linear combination of pure Yang–Mills tree amplitudes with n gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein–Yang–Mills amplitudes with r gravitons and (n−r) gauge bosons as a linear combination of pure Yang–Mills tree amplitudes with n gauge bosons. We present a general formula for this case.