Resummation Approach in QCD Analytic Perturbation Theory

We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start we a simple example of asymptotic ower series for a zero-dimensional analog of the scalar gφ4 model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)PT resummation of nonpower series and provide the one-, two-, and three-loop resummation recipes. We show the results of applications of these recipes to the estimation of the Adler function D(Q2) in the Nf=4 region of Q2 and of the Higgs-boson-decay width ΓH→bb¯(mH2) for MH=100-180GeV2.