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The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguouslyextended to any fixed order of perturbative QCD beyond the so called``large--\beta_0 approximation''. As a result of this procedure, the obtainedperturbation series looks like a continued-fraction representation. Asubsequent generalization of this procedure is developed, in order to optimizethe convergence of the final series, along the lines of the Fastest ConvergencePrescription. This generalized BLM procedure is applied to the Adler D functionand also to R_{e^+e^-} in QCD at N$^3$LO. A further extension of the sequentialBLM is presented which makes use of additional parameters to optimize theconvergence of the power-series at any fixed order of expansion.Comment: 24 pages, JHEP3, 4 figures are enclosed as eps-file, final version to  be published in JHE

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