Some analytic results on the Uehling correction to the g-factor of a boundelectron (muon)

We calculate vacuum-polarization corrections to the g-factor of a bound ele ctron in the ground state of a hydrogenlike atom. The result is found in a closed analytic form for an arbitrary value of the nuclear charge Z. It is valid for both electronic and muonic atoms. Some useful asymptotics are als o presented. The result for the electronic atoms is consistent with publish ed numerical data.