LARGE N-EXPANSION OF QED - ASYMPTOTIC PHOTON PROPAGATOR AND CONTRIBUTIONS TO THE MUON ANOMALY, FOR ANY NUMBER OF LOOPS

We calculate analytical contributions to the n-loop asymptotic photon propagator from diagrams with n-1 electron loops, i.e. the O(1/N) term s in the large N limit. The corresponding contributions to the on-shel l beta-function, beta(alpha) = partial derivative log alpha/partial de rivative log m are reduced to rational combinations of zeta(s) = SIGMA (p) p(-s). For the beta-function of the MOM scheme (i.e. the Gell-Man- Low function) we obtain the O(1/N) terms of PSI(alpha(MOM)) = beta(alp ha) partial derivative log alpha(MOM)/partial derivative log alpha = S IGMA(n) PSI(n)(alpha(MOM)/pi)n in closed form: PSI(n)[n-1] = (n-1)!/(- 3)n-1[-2n+4-n+4/2n +16/n-1 SIGMA/n/2 > s > 0 s(1-2(-2s))(1-2(2s-n))zet a2's+1]. Neglecting terms of order m(e)/m(mu), we calculate (n+1)-loop muon-anomaly contributions, obtained by inserting, in the one-loop di agram, all n-loop photon-propagator diagrams with at least (n-1) elect ron loops. The methods are applicable to any number of loops. Results have been obtained analytically up to 20 loops and numerically up to 1 00 loops.