We consider the three-loop singlet diagrams induced by axial-vector,
scalar and pseudo-scalar currents. Expansions for small and large
external momentum $q$ are presented. They are used in combination
with conformal mapping and Pad\'e approximations in order to arrive at
results for the polarization functions valid for all $q^2$. Results are
presented for the imaginary parts which are directly related to physical
quantities like the production of top quarks or the decay of scalar or
pseudo-scalar Higgs bosons.