  A calculation of the one-loop self-energy and vacuum-polarization corrections
to the hyperfine splitting of the 1s and 2s states in light H-like ions is
carried out to all orders in the parameter Z \alpha. Using the known values for
the Z \alpha-expansion coefficients, the numerical data obtained are
extrapolated from Z=5 and higher to Z=0, 1, and 2, with the resulting accuracy
being significantly better than in previous evaluations. Our calculation shifts
the theoretical value of the normalized difference of the 1s and 2s
hyperfine-structure intervals in ^3He^+ by 0.056 kHz and improves its accuracy.
