  Effects from a finite top quark mass on differential distributions in the
Higgs+jet production cross section through gluon fusion are studied at
next-to-leading order in the strong coupling, i.e. $O(\alpha_s^4)$. Terms
formally subleading in $1/m_t$ are calculated, and their influence on the
transverse momentum and rapidity distribution of the Higgs boson are evaluated.
We find that, for the differential K-factor, the heavy-top limit is valid at
the 2-3% level as long as the transverse momentum of the Higgs remains below
about 150 GeV.
