An analysis is made of the contribution of the polarization of vacuum to th
e hyperfine splitting of the ground state of a hydrogen-like atom. An expre
ssion for the correction to the energy is obtained as an explicit function
of the parameter Z alpha. The final expression derived in terms of generali
zed hypergeometric functions and their derivatives is a function of the par
ticle mass ratio in orbit and in a vacuum loop, and is therefore valid for
both ordinary and muonic atoms. Various asymptotic forms are also given. (C
) MAIK "Nauka/Interperiodica".