SciPost Phys. 19, 057 (2025) ·
published 26 August 2025
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We derive formulae that resum, at a given order in the soft limit, the infinite series of Post-Minkowkian (small gravitational coupling) or Post-Newtonian (small velocities) corrections to the gravitational waveform produced by particles moving along a general (open or closed) trajectory in Schwarzschild geometry in the probe limit. Specifying to the case of circular orbits, we compute the wave form and the energy flux to order 30PN, and compare it against the available results in the literature. The results are based on a novel hypergeometric representation of the solutions of the Heun equation (and its confluence), that leads to a simple mathematical proof of the Heun connection formula.
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