Recently the four-loop perturbative QCD contributions to the relations between pole and running masses of charm, bottom and top quarks were evaluated in the MS-scheme with identical numerical error bars. In this work the flavour dependence of the O(α 4 s ) correction to these asymptotic series is obtained in the semi-analytical form with the help of the least squares method. The numerical structure of the corresponding asymptotic perturbative relations between pole and running c, b and t-quark masses is considered and the theoretical errors of the O(α 4 s )-contributions are discussed. The explicit dependence for these relations on the renormalization scale µ 2 and the flavour number n l is presented.

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