The large top quark mass expansion for Higgs boson decays into bottom quarks and into gluons

We calculate the large top quark mass expansions for the H -> bb_bar decay rate in the order (alpha_s)^2 and for the H -> gluons decay rate in the order (alpha_s)^3. The obtained expansions rapidly converge in the region of their validity, M_H < 2 m_top, i.e. below the threshold of tt_bar production.