Averages Over Portions of Configuration Space

The integral $\int {\gamma }^{\delta }{R_{\mathrm{nl}}}^2{\rho }^{\sigma +2\mathrm{}}d\rho$ is evaluated where $R_{\mathrm{nl}}$ is the radial hydrogen eigenfunction. The results are applied to the calculation of term shifts when the Born-Infeld potential function replaces the Coulomb potential function in the one-electron Schroedinger problem.