  State-dependent quantum electrodynamic corrections are evaluated for the
hyperfine splitting of nS states for arbitrary principal quantum number n. The
calculations comprise both the self-energy and the vacuum-polarization
correction of order alpha(Z alpha)^2 E_F and the recoil correction of order (Z
alpha)^2 (m/M) E_F. Higher-order corrections are summarized and partly
reevaluated as well. Accurate predictions for hydrogen hyperfine splitting
intervals of nS states with n=2,...,8 are presented. The results obtained are
important due to steady progress in hydrogen spectroscopy for transitions
involving highly excited S states.
