  The technique of conformal mappings is applied to enlarge the convergence of
the Borel series and to accelerate the convergence of Borel-summed Green
functions in perturbative QCD. We use the optimal mapping, which takes into
account the location of all the singularities of the Borel transform as well as
the present knowledge about its behaviour near the first branch points. The
determination of \alpha_{s}(m_{\tau}) from the hadronic decay rate of the
\tau-lepton is discussed as an illustration of the method.
