Nonpower expansions for QCD observables at low energies

A comprehensive review is presented of the progress made in further developing the ghost-free Analytic Approach to low-energy QCD since “QCD-97” meeting. It is now formulated as a logically closed “Analytic Perturbation Theory” algorithm. Its most essential feature is nonpower functional expansions for QCD observables.Nonpower expansion functions are oscillating in the low energy domain, where the QCD coupling is not weak. This effect suppresses the influence of higher-loop contributions that, in turn, diminishes the scheme dependence and improves the convergence property of perturbative expansion for observables.