Radiative-nonrecoil corrections of order alpha² (Z alpha) E_F to the hyperfine splitting of muonium

We present results for the corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We improve the precision of previous results.