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Zusammenfassung:
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 (Z)2EF and the recoil correction of order (Z)2(m/M)EF. 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.