  Using the parallel/orthogonal space method, we calculate the planar two-loop
three-point diagram and two rotated reduced planar two-loop three-point
diagrams. Together with the crossed topology, these diagrams are the most
complicated ones in the two-loop corrections necessary, for instance, for the
decay of the Z^0 boson. Instead of calculating particular decay processes, we
present the new algorithm which allows one to calculate arbitrary NNLO
calculations for massive planar two-loop vertex functions in the general mass
case. All integration steps up to the last two ones are performed analytically
and will be implemented under xloops as part of the Mainz xloops-GiNaC project.
The last two integrations are done numerically using methods like VEGAS and
Divonne. Thresholds originating from Landau singularities are found and
discussed in detail. In order to demonstrate the numeric stability of our
methods we consider particular Feynman integrals which contribute to different
physical processes. Our results can be generalized to the case of the crossed
topology.
