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Results on the resummation of non-power-series expansions of the Adlerfunction of a scalar, $D_S$, and a vector, $D_V$, correlator are presentedwithin fractional analytic perturbation theory (FAPT). The first observable canbe used to determine the decay width $\Gamma_{H\to b\bar{b}}$ of a scalar Higgsboson to a bottom-antibottom pair, while the second one is relevant for the$e^+e^-$ annihilation cross section. The obtained estimates are compared withthose from fixed-order (FOPT) and contour-improved perturbation theory (CIPT),working out the differences. We prove that although FAPT and CIPT areconceptually different, they yield identical results. The convergenceproperties of these expansions are discussed and predictions are extracted forthe resummed series of $R_S$ and $D_V$ using one- and two-loop couplingrunning, and making use of appropriate generating functions for thecoefficients of the perturbative series.

Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT