  In this paper we consider the next-to-next-to-leading order total cross
section of Higgs boson pair production in the large top quark mass limit and
compute four expansion terms in $1/m_t^2$. Good convergence is observed below
the top quark threshold, which makes our results a valuable input for
approximation methods which aim for next-to-next-to-leading order corrections
over the whole kinematic range. We present details on various steps of our
calculation; in particular, we provide results for three- and four-particle
phase-space master integrals and describe in detail the evaluation of the
collinear counterterms.
