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impossible

ok i'll start by first conjecture, is it infinity ?

It's not, it actually converges to a finite number in the complex plane.

oh wait as n goes to infinity i thought as x goes to :P

\[u = e^u\]

wolfram gives answer in terms of product log function

I suppose that's as closed as it's going to get :)

\[\lim_{n\to\infty} \underbrace{\ln(\ln(\cdots\ln x))}_{n\text{ times}} = -W_k(-1)\]

If it helps, the approximate value of the limit is \(0.318132+1.33724 i\).

Whoops I also made a mistake and wrote \(e^{i \pi}\) when it should be \(e^{i \pi/2}\)