The technique of conformal mapping is applied to enlarge the convergence domain 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 behavior near the first branch points. The determination of ${\alpha }_s{(m}_{\tau }^2)$ from the hadronic decay rate of the $\tau$ lepton is discussed as an illustration of the method.

• Received 20 November 1998

DOI:https://doi.org/10.1103/PhysRevD.60.054014