Searching for an asymptotic to exp[0.5]

[JmsNxn]

So, anyway, lets say we have these zeros of the asymptotic half iterate in an infinite list. Can we recover the asymptotic half iterate with the Weiestrass factorization theorem?
- Sheldon

If you have some more to add on top of the theorem. All it will give you is the half iterate upto multiplication by an entire never zero function. These are usually solved using additional properties of the function. I'm sure there must be a way.