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

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=${\mathcal{J}}_{n=0\mathrm{}}^{\infty }$ $c_n$(α/π${)}^n$ 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 α. These convergence acceleration methods also provide as estimates of the higher-order expansion coefficients $c_4$=-5.65±0.64, $c_5$=31±6. .AE