Corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the muon anomaly from fourth-order electron vacuum polarization is determined to order $\frac{m_e}{m_{\mu }}$. The result, including the contribution from graphs containing two second-order lepton vacuum polarization subgraphs is ${\left(\frac{\alpha }{\pi }\right)}^3\left[\right(\frac{2}{9}\left){\ln }^2\right(\frac{m_{\mu }}{m_e})+(\frac{403}{108}-\frac{4{\pi }^2}{9}\left)\ln \right(\frac{m_{\mu }}{m_e})+\frac{\zeta \mathrm{}\left(3\right)\mathrm{}}{2}+\frac{2{\pi }^2}{27}+\frac{5}{27}-6.56\mathrm{}\frac{m_e}{m_{\mu }}]$.