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We present an extension of work in an earlier paper showing high precisioncomparisons between black hole perturbation theory and post-Newtonian (PN)theory in their region of overlapping validity for bound, eccentric-orbit,Schwarzschild extreme-mass-ratio inspirals. As before we apply a numericalfitting scheme to extract eccentricity coefficients in the PN expansion of thegravitational wave fluxes, which are then converted to exact analytic formusing an integer-relation algorithm. In this work, however, we fit toindividual $lmn$ modes to exploit simplifying factorizations that lie therein.Since the previous paper focused solely on the energy flux, here we concentrateinitially on analyzing the angular momentum flux to infinity. A first stepinvolves finding convenient forms for hereditary contributions to the flux atlow-PN order, analogous to similar terms worked out previously for the energyflux. We then apply the upgraded techniques to find new PN terms through 9PNorder and (at many PN orders) to $e^{30}$ in the power series in eccentricity.With the new approach applied to angular momentum fluxes, we return to theenergy fluxes at infinity to extend those previous results. Like before, theunderlying method uses a \textsc{Mathematica} code based on use of theMano-Suzuki-Takasugi (MST) function expansion formalism to representgravitational perturbations and spectral source integration (SSI) to findnumerical results at arbitrarily high precision.

physical review. d/physical review. d.

Determination of new coefficients in the angular momentum and energy  fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio  inspirals using mode-by-mode fitting