  The virtual corrections to $gg\to HH$ and $gg\to ZH$ are analytically
evaluated combining an expansion in the small transverse momentum of the final
particles with an expansion valid at high energies. The two expansion methods
describe complementary regions of the phase space and we merge their results,
extending the range of validity of both expansions using Pad\'e approximants.
We show that this approach can reproduce the available numerical results
retaining the exact top quark mass dependence with an accuracy well below the
1% level. Our results allow a fast and flexible evaluation of the virtual
corrections of the considered processes. Furthermore, they are available in
different renormalisation schemes of the top quark mass.
