In this work, we develop analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We also derive the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we construct an end point-constrained analytic approximation that significantly accelerates the computation of the Fourier modes at large eccentricity. The overall error of this analytic approximation is controlled within ${10}^{-3}$, and it remains valid for Fourier modes with $p\le 200$ and $e\le 0.9$. This approach provides analytic building blocks for modeling frequency-domain gravitational waves from highly eccentric binaries.

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• General relativity
• Gravitation
• Gravitational wave detection
• Gravitational wave sources
• Gravitational waves