closed form for regular superfunction expressed as a periodic function

[sheldonison]

dear sheldon , i think you are confused because exp(x) - 1 doesnt have a holomorphic half-iterate.

regards

tommy1729

I think I'll need to get Peter Walker's paper, Proc. AMS 1990. He proved that the upper superfunction of exp(x)-1 is entire, which corresponds to the upper superfunction of \( \eta \). I would be interested in knowing how that was done.

My understanding is that there is a analytic half-iterate of exp(x)-1, but it isn't entire.
- Sheldon