Nixon-Banach-Lambert-Raes tetration is analytic , simple and “ closed form “ !!

[tommy1729]

Hey, Tommy!

So I had noticed that you implicitly assumed \( V(s+1) = V(s) \) in your original analysis. I didn't notice it right away, but I noticed it afterwards when I saw it would imply \( 2 \pi i \) periodicity. I looked at it some more, and was pretty sure you were on to something--but never been too good with the Lambert function. This makes much much more sense quite frankly. Especially if we think of the branch cuts appearing at \( \Im(s) = 2\pi k \) for \( k \in \mathbb{Z} \). This is where our \( \phi \) function will recycle, and a cluster of singularities will force non-analycity of \( \tau \). 

Now I am confused.
You say non-analytic here.
And you also wrote 2 papers claiming analytic ?

Im aware of Sheldon's arguments and the complexity of tetration.
But the point is I am confused about your viewpoint.

I mean non-analycity of \( \tau \) would imply non-analytic tetration right ?
But you have 2 papers claiming analyticity and intend to explain it further.

Regards

tommy1729