Abstract
We apply the Euler transformation to accelerate the convergence of the QCD perturbative series with the aim to determine the strong coupling αs in terms of the total τ-decay rate rτ. The variation of the result with the order of the QCD perturbation theory is small and comparable with the uncertainties of rτ. We also present an estimate of a range of the yet unknown 5th and 6th order coefficients k5 and k6 of the Adler function.
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