regular tetration at b=e^(-e)

[bo198214]

I'm not sure if or how this would carry over to/affect the Schroeder function.

You mean the Abel function? Schroeder function occurs only for fixed points p with |f'(p)|=0,1.

I've heard that the series obtained for \( f^t(z) \) for \( f(z) = u^z - 1 \) with respect to z at z = 0 do not converge but diverge and diverge very strongly.

This is true (provably true, there are only few exception of f'(0)=1 that converge). It was not completely clear to me whether this would affect the convergence of the powerseries in the Abel function. But it seems that it is also divergent, perhaps I can prove that in a next post.

But this does not destroy us:
1. Often divergent series reach more quickly usable values than convergent series if you truncate in the right moment.
2. With help of the above formula there is a (dog-slowly but converging) limit formula.