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We obtain generalised power series expansions for a family of planar two-loopmaster integrals relevant for the QCD corrections to Higgs + jet production,with physical heavy-quark mass dependence. This is achieved by definingdifferential equations along contours connecting two fixed points, and bysolving them in terms of one-dimensional generalised power series. Theprocedure is efficient and can be repeated in order to reach any point of thekinematic regions. The analytic continuation of the series is straightforwardand we present new results below and above the physical thresholds. The methodwe use allows to compute the integrals in all kinematic regions with highprecision. Performing a series expansion on a typical contour above thephysical threshold takes on average $\mathcal{O}(1 \text{ second})$ perintegral with worst relative error of $\mathcal{O}(10^{-32})$, on a single CPUcore. After the series is found the numerical evaluation of the integrals inany point of the contour is virtually instant. Our approach is general and canbe applied to Feynman integrals provided that a set of differential equationsis available.

Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops