Searching for an asymptotic to exp[0.5]

[sheldonison]

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.

Thanks James,

It looks like the "multiplication by an entire never zero function" is exp(g(z)), where g(z) is any entire function. For our purposes, g(z)=k might work, if that is a legal choice. That would just be multiplication by a constant. Multiplication by exp of anything else would probably grow faster than the half iterate of exponentiation, which by definition grows slower than exp(z).
- Sheldon