THE ANALYTICAL CONTRIBUTION OF THE 3-LOOP DIAGRAMS WITH 2 FERMION CIRCLES TO THE PHOTON PROPAGATOR AND TO THE 8TH-ORDER CORRECTION TO THE MUON ANOMALOUS MAGNETIC-MOMENT

Using the renormalization group relations between the QED-beta-functions in different renormalization schemes and the previously obtained result for the four-loop contribution to the beta-function in the on-shelf scheme-beta-os we obtain the analytical contributions of the three-loop QED diagrams with two fermion circles to the photon vacuum polarization function in the on-shell scheme and to the eight-order correction to the muon anomalous magnetic moment a-mu. The result for a-mu-disagrees with the result of the recent numerical computations. The origin of this disagreement is commented on. The corrected expression for the cubic in the contribution of the number of leptons to the QED-beta-os-function is presented.