Hi Sheldon -

thanks for your comment. What remains for me is, whether my impression, that the Kneser-method and the polynomial-method ("quick&dirty-eigendecomposition") approximate if I increase the size of the truncation of the Carlemanmatrix. That would be a really remarkable statement!

It would raise the subsequent question, whether the triangular Carleman-matrix, which results from the fixpoint-shift and gives the basis for the regular tetration, or its triangular eigenmatrices, simply need some completion factor, perhaps something like the integral in the Ramanujan-summation for the divergent series to agree with the two other results... I am in search of such a thing for long but with no avail so far - perhaps from the current observation one can get a hint where to dig?

Gottfried

thanks for your comment. What remains for me is, whether my impression, that the Kneser-method and the polynomial-method ("quick&dirty-eigendecomposition") approximate if I increase the size of the truncation of the Carlemanmatrix. That would be a really remarkable statement!

It would raise the subsequent question, whether the triangular Carleman-matrix, which results from the fixpoint-shift and gives the basis for the regular tetration, or its triangular eigenmatrices, simply need some completion factor, perhaps something like the integral in the Ramanujan-summation for the divergent series to agree with the two other results... I am in search of such a thing for long but with no avail so far - perhaps from the current observation one can get a hint where to dig?

Gottfried

Gottfried Helms, Kassel