  We determine the three-loop form factor parameterising the amplitude for the
production of an off-shell Higgs boson in gluon fusion in QCD with a single
massive quark. The result is obtained via a numerical solution of a system of
differential equation for the occurring master integrals. The solution is also
used to determine the high-energy and threshold expansions of the form factor.
Our findings may be used for the evaluation of virtual corrections generated by
top-quark and b-quark loops in Higgs boson hadroproduction cross sections at
next-to-next-to-leading order.
