Of course, as soon as I post this I've essentially proved it using the Fourier expansion. Now I'm just hoping Sheldon comes on and can enlighten me a bit more as to why this works.

First and foremost

where

and

If is the inverse schroder function, normalized so that , then

where

and, as Sheldon mentions, but I haven't seen a fully rigorous proof,

for

therefore . Now it follows that

and tetration is contained in a disk about that lies in the right half plane.

NOW, all I need is for . Sheldon has claimed this, but in order to put it in the paper, I'll probably either need to prove it myself, or have a good reference. In a short enough, well thought out manner, that is rigorous enough to put in the finalized version of my paper (credit will be given, of course).

First and foremost

where

and

If is the inverse schroder function, normalized so that , then

where

and, as Sheldon mentions, but I haven't seen a fully rigorous proof,

for

therefore . Now it follows that

and tetration is contained in a disk about that lies in the right half plane.

NOW, all I need is for . Sheldon has claimed this, but in order to put it in the paper, I'll probably either need to prove it myself, or have a good reference. In a short enough, well thought out manner, that is rigorous enough to put in the finalized version of my paper (credit will be given, of course).