The vacuum polarization functions $\Pi(q^2)$ of charged and neutral
gauge bosons which arise from top and bottom quark loops lead to
important shifts in relations between electroweak parameters
which can be measured with ever-increasing precision. The large
mass of the top quark allows approximation of these functions through
the first two terms of an expansion in $M_Z^2/M_t^2$.
The first three terms of the Taylor series of $\Pi(q^2)$ are
evaluated analytically up to order $\as^2$.
The first two are required to derive the approximation, the
third can be used to demonstrate the smallness of the neglected terms.
The paper
improves earlier results
based on the leading term $\propto G_F M_t^2 \as^2$.
Results for the subleading
contributions to $\dr$ and the effective mixing angle $\sineff$ are presented.
