Estimates of the electrongfactor: Application of convergence acceleration methods to the QED series

Abstract

We have applied a variety of different convergence acceleration methods to the accurately known (first four) terms of the QED perturbation series for the electron g factor g/2=${\mathcal{J}}_{n=0}^{\ensuremath{\infty}}$${c}_{n}$(\ensuremath{\alpha}/\ensuremath{\pi}${)}^{n}$ so as to obtain eight estimates of its value. All of the estimates agree with the most recent experimental value of g/2 to better than one standard deviation when we use the new NBS condensed-matter value of \ensuremath{\alpha}. These convergence acceleration methods also provide as estimates of the higher-order expansion coefficients ${c}_{4}$=-5.65\ifmmode\pm\else\textpm\fi{}0.64, ${c}_{5}$=31\ifmmode\pm\else\textpm\fi{}6. .AE