Gravitational-wave fluxes from eccentric orbits, solved analytically

Modeling extreme-mass-ratio inspirals (EMRIs) for LISA requires precise gravitational-wave flux calculations across a wide range of orbital shapes, but most analytic approaches break down at high eccentricity. By expanding Fourier coefficients of the emitted radiation in a Chebyshev basis and connecting them to results from the Quantum Spectral Method, this work sidesteps that limitation entirely. Tested against a 15th-order post-Newtonian input, the method achieves relative errors below 10⁻⁵ for moderately eccentric orbits and below 10⁻⁶ mode-by-mode for strongly eccentric strong-field cases. The result is a fully analytic frequency-domain pipeline directly applicable to EMRI waveform modeling.