Generalization of the BLM procedure and its scales in any order of pQCD

The Brodsky-Lepage-Mackenzie procedure is sequentially and unambiguoulsy extended to any fixed order of perturbative QCD beyond the so called large-beta(0) approximation. As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to Re+e- in QCD at (NLO)-L-3. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.