Gravitational microlensing source limb-darkening and   limb-polarization,~I: angle-averaged amplification functions
  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. 
Norman Gray (University of Glasgow, UK)