Three-loop polarization function and O( αs2) corrections to the production of heavy quarks

The three-loop vacuum polarization function Π( q²) induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the O( α_s²) result for the production of heavy quarks R( s) = σ( e⁺e^- → hadrons)/ σ( e⁺e^- → μ⁺μ^-) can be extracted. Explicit formulae separated into the different colour factors are given.