Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki, and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimized method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of l, and in doing so develop an efficient new method for generating the MST renormalized angular momentum, nu.