Three-Loop Polarization Function and ${\cal O}(\alpha_s^2)$ Corrections   to the Production of Heavy Quarks
  The three-loop vacuum polarization function $\Pi(q^2)$ induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the ${\cal O}(\alpha_s^2)$ result for the production of heavy quarks $R(s)=\sigma(e^+e^-\to \mbox{hadrons})/\sigma(e^+e^-\to \mu^+\mu^-)$ can be extracted. Explicit formulae separated into the different colour factors are given. 
K.G. Chetyrkin (MPI f\"ur Physik, Munich, Germany), J.H. Kuehn, M.   Steinhauser (Uni. Karlsruhe, Germany)