Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop   beta-function and the muon anomaly
  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. 
D.J. Broadhurst, A.L. Kataev and O.V. Tarasov