====== TTP96-13 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, J.H. Kuehn, M. Steinhauser** | |** Nucl. Phys. B482 213-240 1996 ** | | {{preprints:1996:ttp96-13.pdf|PDF}} {{preprints:1996:ttp96-13.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9606230|arXiv]] | | |