Eccentric-orbit extreme-mass-ratio inspiral gravitational wave energy fluxes to 7PN order

We present new results through 7PN order on the energy flux from eccentric extreme-mass-ratio binaries. The black hole perturbation calculations are made at very high accuracy (200 decimal places) using a Mathematica code based on the Mano-Suzuki-Takasugi analytic function expansion formalism. All published coefficients in the expansion through 3PN order at lowest order in the mass ratio are confirmed and new analytic and numeric terms are found to high order in powers of e^2 at post-Newtonian orders between 3. 5PN and 7PN. We also show original work in finding (nearly) arbitrarily accurate expansions for hereditary terms at 1. 5PN, 2. 5PN, and 3PN orders. An asymptotic analysis is developed that guides an understanding of eccentricity singular factors, which diverge at unit eccentricity and which appear at each PN order. We fit to a model at each PN order that includes these eccentricity singular factors, which allows the flux to be accurately determined out to e1.