Fractional iteration of x^2+1 at infinity and fractional iteration of exp

[Gottfried]

This may lead into a new way of computing fractional iterates of exp, because we just approximate exp(x) with polynomials \( \sum_{n=0}^N \frac{x^n}{n!} \) and approximate the half-iterate of exp with the half-iterate of these polynomials.

As I read somewhere, best mathematical solutions are the simple, elegant ones. It would be great if this proves to be such an approach... This'll give me stuff to chew on for the weekend :-)

Gottfried