This seems a bit icky as you move away from the origin. There’s no promises for how fast the series converges and how well it does yea far out and so on and so

This seems a bit icky as you move away from the origin. There’s no promises for how fast the series converges and how well it does yea far out and so on and so forth. This reminds me a bit of harmonic balance which is a great, well behaved spectral technique