  We present the results of analytical calculations of the 3-loop contributions
to the asymptotic photon vacuum polarization function, in the on shell scheme,
and of the 4-loop contributions to the on shell QED beta-function. These are
used to evaluate various 4-loop and 5-loop contributions to the muon anomaly.
Our analytical contributions to (g-2)_\mu differ significantly from previous
numerical results. A very recent numerical re-evaluation of 4-loop muon-anomaly
contributions has yielded results much closer to ours.
