Three-loop polarization function and O(alpha(2)(s)) 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 O(alpha(s)(2)) result for the production of heavy quarks R(s) = sigma(e(+)e(-) --> hadrons)/sigma(e(+)e(-) --> mu(+)mu(-)) can be extracted. Explicit formulae separated into the different colour factors are given.