Precise mass-dependent QED contributions to leptonicg−2at orderα2andα3

Improved values for the two- and three-loop mass-dependent QED contributions to the anomalous magnetic moments of the electron, muon, and $\tau$ lepton are presented. The standard model prediction for the electron ($g-2$) is compared with its most precise recent measurement, providing a value of the fine-structure constant in agreement with a recently published determination. For the $\tau$ lepton, differences with previously published results are found and discussed.