Revisting my accelerated slog solution using Abel matrix inversion

[jaydfox]

The good news is, the acceleration can be taken a step further, by removing the algebraic singularity that remains after removing the logarithmic singularity.  A few years ago, I determined that my accelerated solution appears to be converging on an algebraic singularity in terms of \( (z-L)^{2\pi i / L} \), or rather a power series in such.  (I typically call the fixed point a in my code, but I'm using L here, since that's what you mentioned in your post.)

I can't remember now if the exponent for the algebraic term is 2*pi*i/L, or if it's the reciprocal, L/(2*pi*i).  I apologize if I had the fraction upside down.  I don't have my notes in front of me, so I'm doing this from memory.  When I get around to posting more details on the algebraic singularity, I'll be sure to clarify the exponent and provide a proof.