12/27/2015, 11:15 AM

(12/24/2015, 03:25 AM)sheldonison Wrote: And the formal half iterate begins with

Ok, so I replaced y with 1/2 and log(L) with L in the regular iteration power series to get this:

as expected it's the same power series.

I wanted to highlight one of my findings in this paper (page 12) that is related but separate from this, which is a power series for for any analytic function with a parabolic fixed point at 0.

Substituting in we get

which I realize is a different base, but still interesting.

Using a similar technique, we might be able to find a comparable power series for , at which point would at the very least intersect with this function.