Analytic Calculation to all Orders inZαof Nuclear Size Effects in Vacuum Polarization

We have calculated the change in the vacuum polarization for muonic atoms with a high-$Z$ nucleus arising from the finite extent of its charge distribution. In the calculation, the electron mass is set equal to zero and only the first term in an expansion in (nuclear radius)/(radius of the muonic state) is retained. The calculation is done to all orders in $Z\alpha$ and a simple closed-form result is obtained.