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Perturbative relations between pole and running heavy quark masses, definedin the Minkowski regions, are considered. Special attention is paid to theappearance of the kinematic $\pi^2$-effects, which exist in the coefficients ofthese series. The estimates of order $O(\alpha_s^4)$ QCD corrections arepresented.

Peculiar features of the relations between pole and running heavy quark masses and estimates of the O(\alpha_s^4) contributions