Iterability of exp(x)-1

[bo198214]

My point, which should have been very clear, is that a function can be continued by analytic extension, even if its power series fails to converge for inputs that should be non-singular values.

But the claim was about entirety, there is not "a bit entire" and "quite entire". Analytic extension is not necessary there. If a function is entire the powerseries converges at each point. If it does not, maybe we can help ourselves by analytic extension but it is not entire then.