An analytic function expansion approach to computing perturbations from extreme-mass-ratio binaries with eccentric orbits

Several groups (Fujita 2012; Shah, Friedman, and Whiting 2014; Shah 2014; Fujita 2014) have recently described results from computing gravitational perturbations and the self-force at extraordinarily high precision for binaries with circular orbits in the extreme-mass-ratio limit. These calculations have allowed comparison with post-Newtonian (PN) theory at the lowest order in the mass ratio and uncovered new terms and coefficients in the PN expansion for circular orbits. We describe a new means of extending this analytic function expansion approach to include binaries with eccentric orbits, thus allowing terms in the known 3PN order expansion to be verified and to discover new terms beyond 3PN.