  We present new results on the summation of nonpower-series expansions in QCD
Analytic Perturbation Theory (APT) in the one-loop approximation. We show how
to generalize the approach suggested by one of us earlier to the cases of APT
and Fractional APT (FAPT) with heavy-quark thresholds. Using this approach we
analyze the Higgs boson decay $H^0\to\bar{b}b$. We produce estimations of the
higher-order corrections importance in (F)APT and present a very transparent
interpretation of the resummation results in terms of $\Lambda_\text{QCD}$
shifts.
