  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 optimised 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 $\ell$, and in
doing so develop an efficient new method for generating the MST renormalised
angular momentum, $\nu$.
