On dependence of nonperturbative contributions in $\bar\alpha_s(q^2)$ on   an initial approximation of perturbation theory in an analytic approach to   QCD
  In the framework of analytic approach to QCD, which has been recently intensively developed, the dependence of nonperturbative contributions in a running coupling of strong interaction on initial perturbative approximation to 3-loop order is studied. The nonperturbative contributions are obtained in an explicit form. In the ultraviolet region they are shown to be represented in the form of the expansion in the inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors $n_f$ and for different numbers of loops taken into account. For all $n_f$ of interest it is shown that 2-loop order and 3-loop order corrections result in partial compensation of 1-loop order leading in the ultraviolet region nonperturbative contribution. 
Aleksey I. Alekseev