Continuum sum - a new hope

[bo198214]

Henryk,
Could you clarify what function you are referring to that is not analytic? I thought that regular tetration developed from the complex fixed point for base e, with complex values on the real number line, was analytic and entire. It must have something to do with the rest of this post....
- Sheldon

I am referring to the regular Abel function at the primary fixed point.
The inverse function (regular superfunction) is entire. But the Abel function has singularities on the real line at \( \exp^{[n]}(0) \), \( n\in \mathbb{N} \).