Renormalization group improvement of truncated perturbative series in QCD. Decays of tau-lepton and eta_c-charmonium

We formulate a general scheme to improve the truncated perturbative expansion in alpha_s by means of the renormalization group in QCD for the single-scale quantities. The procedure is used for the evaluation of hadronic decay rates of tau-lepton and eta_c-charmonium. The scale dependence of result for eta_c is studied in the scheme of fixed value for the MS-bar mass of charmed quark.