bo198214 Wrote:Guys! That I didnt see that before!

We have a very simple formula for computing the -th iterate of an arbitrary function:

I want to add, that this expression exites me very much.

Just these days I was looking for alternatives (hopefully improvements) of our fractional iteration problem.

I was looking for two aspects

- expression of the tetration by its own powertowers instead of powerseries

- interpolation not done based on polynomial interpolation of the coefficients of the powerseries but based on an interpolation of gamma

The first is obvious; the idea is that only values are involved, which are provided by the function itself (so, for instance, possibly only of a relevant subset of complex numbers which are accessible by the function and its iterates itself/themselves - hmm, amateurish expressed; I hope the idea behind this can be understood anyway)

The second, because the fractional binomials use gamma of fractional parameters.

So - in my view - this is a big shot...

Gottfried

Gottfried Helms, Kassel