  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 (MST) analytic function expansion formalism. All
published coefficients in the expansion through 3PN order are confirmed and new
analytic and numeric terms are found to high order in $e^2$ at 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. We
fit to a model where at each PN order an eccentricity singular function is
factored out, improving substantially the fit even as $e \to 1$.
