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We give a short introduction to the Analytic Perturbation Theory (APT) andits generalization to Fractional powers -- FAPT. We describe how to treatheavy-quark thresholds in FAPT and then show how to resum perturbative seriesin both the one-loop APT and FAPT. As an application we consider FAPTdescription of the Higgs boson decay $H^0\to b\bar{b}$.

Resummation in Fractional APT: How many loops do we need to take into account?