  We present analytic results for one-loop Higgs boson + $n$-gluon amplitudes
for $n\le 5$ in the full theory including all dependence on the (top) quark
mass. In this paper we consider only the case where the gluons all have the
same helicity. The amplitudes are expressed in simple formula and display
similar structure. Their limiting behaviour in small Higgs momentum and large
top mass is studied.
