R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms

High-energy behavior of R-ratio of electron-positron annihilation into hadrons is studied. In particular, it is argued that at any given order of perturbation theory the re-expansion of the R-ratio in the ultraviolet asymptotic can be reduced to the form of power series in the naive continuation of the strong running coupling into the timelike domain. The convergence range of the re-expanded R-ratio and the corresponding higher-order pi2-terms are discussed.