Vacuum polarization in a hydrogen-like relativistic atom: g factor of a bound electron

The contribution of vacuum polarization to the g factor of a bound electron is considered for the ground state of a hydrogen-like atom. A final expression for the correction is obtained in terms of generalized hypergeometric functions and represents a function of parameter Zα and the ratio of the mass of the orbital particle (electron or muon) to the mass of a particle in the vacuum loop. Different asymptotic forms of this expression are derived for both common and muon atoms.