  We propose a novel method for the treatment of top-quark mass effects in the
production of $H^{(*)}$, $HH$, $HZ$ and $ZZ$ final states in gluon fusion. We
show that it is possible to reconstruct the full top-quark mass dependence of
the virtual amplitudes from the corresponding large-$m_t$ expansion and the
non-analytic part of the amplitude near the top-quark threshold
$\hat{s}=4m_t^2$ with a Pad\'e ansatz. The reliability of our method is clearly
demonstrated by a comparison with the recent NLO result for Higgs pair
production with full top-quark mass dependence.
