  There is increasing interest in extended source effects in microlensing
events, as probes of the unresolved sources. Previous work has either presumed
a uniform source, or else required an approximate or numerical treatment of the
amplification function averaged over the source disk. In this paper, I present
analytic expressions for the angle-averaged amplification functions for the
rotationally-symmetric intensity and polarization cases.
  These integrals will allow us to use the technology of inverse problems to
study the source limb-darkening and limb-polarization functions.
