Revisting my accelerated slog solution using Abel matrix inversion

[jaydfox]

The main region matches Jay's slog series to better than 76 decimal digits inside most of the circle!  The results are so good that for all intents and purposes, the two functions are the same, except near the two singularities as can be seen from the image.  Even near the singularity but before it turns black, at z=i, the two match each other to within 5E-74.  The plot turns black when consistency is below ~70 decimal digits and consistency is better than 5E-64 everywhere in the circle of radius 1.1.  As before, I am using the first 692 Taylor series coefficients of Jay's slog, where a_692~=2E-111.

Hi Sheldon, I had noticed that the accuracy you mentioned (76 digits) was really close to 256 bits.  I perhaps read your post too quickly, and I assumed this limitation in accuracy was in your solution.  But it finally dawned on me that this limitation was in my solution, or rather in the coefficients I posted.

If you were at all interested in doing this analysis again, with higher precision, I am attaching the first 800 coefficients of my 4096-term solution, to 1024 bits of precision.  (Based on my previous research, my matrix solver loses about 11 bits of precision for every 8 terms I add.  I started with 7168 bits, and lost about 4096*11/8 bits, leaving about 1536 bits, though this is only an estimate.  I'm reasonably confident that the first 1300-1400 bits are precise, so these 1024-bit terms should have full precision.)