10/16/2013, 05:07 PM

(10/16/2013, 04:12 PM)sheldonison Wrote: The difference between your taylor series, and the Kneser solution taylor series is reasonably small. All the coefficients differ by less than 2.5^10-6. To me, it does indeed look like the Kneser solution, both in the complex plane and the real axis. (...)Well, this is going to become ironic somehow... That "polynomial interpolation" was my very first and naive approach to the tetration (see my first messages here in the board) and then I felt its model was too unspecific and did a big exploration until I arrived at the regular tetration with the Carleman-matrix (which I called "Matrixoperator" not knowing they are already well studied) including the series-recentering towards the fixpoint and then eigendecomposition - just to come back to the beginning and meet ol' Hellmuth Kneser there...

Sometimes things go strange...

Gottfried

Gottfried Helms, Kassel