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The next-next-to-leading order QCD corrections to the e+e- annihilation intohadrons are considered. The stability of the predictions with respect to changeof the renormalization scheme is discussed in detail for the case of five, fourand three active quark flavors. The analysis is based on the recently proposedcondition for selecting renormalization schemes according to the degree ofcancellation that they introduce in the expression for the scheme invariantcombination of the expansion coefficients. It is demonstrated that the schemedependence ambiguity in the predictions obtained with the conventionalexpansion is substantial, particularly at lower energies. It is shown however,that the stability of the predictions is greatly improved when QCD correctionsare evaluated in a more precise way, by utilizing the contour integralrepresentation and calculating numerically the contour integral.Comment: 23 pages in LateX, 15 PostScript figures in tarred, gzipped and  uuencoded file. Misprint in Eq.6 has been corrected, two references added,  and a comment on related paper include

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Improved evaluation of the next-next-to-leading order QCD corrections to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>annihilation into hadrons

Improved evaluation of the next-next-to-leading order QCD corrections toe+e−annihilation into hadrons