07/04/2022, 01:12 PM
(07/04/2022, 11:10 AM)Gottfried Wrote: TPID 18: Is "polynomial" tetration (by truncated Carleman-matrices) of some order \(n\) with \( n \to \infty \) asymptotic to the Kneser-solution?
This is a long outstanding problem of mine. I've some numerical examples since years which seem to suggest that, but had never an idea how to approach at all a proof/disproof of such a conjecture.
One example where I worked with this is here but I've some more material of comparision in my local excel- and Pari/gp-files which might be worked out further.
My examples with truncations of the Carlemanmatrices from sizes \(4 \times 4,8 \times 8,16 \times 16,32 \times 32 \) up to \(64 \times 64 \) with some random chosen small bases (like \(b=\sqrt 2 , b=4 , b=e \) ) show nice improvement of approximations to 5 or 10 ore more correct digits.
sorry to ask here , but has it been proven that all rising integer sequences (of size) give the same result ?
regards
tommy1729