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Recent analytical and numerical results for the three-loop polarizationfunction allow to present a phenomenological analysis of the cross section formassive quark production in electron positron annihilation to order$\alpha_s^2$. Numerical predictions based on fixed order perturbation theoryare presented for charm and bottom production above 5 and 11.5 GeV,respectively. The contribution from these energy regions to $\alpha(M_Z^2)$,the running QED coupling constant at scale M_Z, are given. The dominant termsclose to threshold, i.e. in an expansion for small quark velocity $\beta$, arepresented.Comment: 26 pages (Latex), 16 figures (Postscript

Massive quark production in electron positron annihilation to order $\alpha_s^2$