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In this work we examine the Cauchy convergence of both post-Newtonian(T-approximant) and re-summed post-Newtonian (P-approximant) templates for thecase of a test-mass orbiting a Kerr black hole along a circular equatorialorbit. The Cauchy criterion demands that the inner product between the $n$ and$n+1$ order approximation approaches unity, as we increase the order ofapproximation. In previous works, it has been shown that we achieve greaterfitting factors and better parameter estimation using the P-approximanttemplates for both Schwarzschild and Kerr black holes. In this work, we showthat the P-approximant templates also display a faster Cauchy convergencemaking them a superior template to the standard post-Newtonian templates.Comment: 5 pages, Replaced with shortened published versio

The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems