Effective coupling constant expansion of the muon anomalous magnetic moment

The relationship between the renormalization group and the muon anomalous magnetic moment calculation in QED is reconsidered. A very simple analysis shows that the contribution to the muon anomaly from muon vertex graphs with electron loop insertions in the photon propagators is function of only one dimensionless effective coupling constant $\text{α}{}_{\mathrm{\mu }}\text{?}\text{1}\text{136.0785}$. The perturbative expansion coefficients up to the α³_μ term are given, and comparison is made with the previous calculations.