Could be tetration if this integral converges

[mike3]

And by the asymptotics of \( \Gamma \) as \( R \to \infty \) we get!

\( \frac{1}{2\pi i}\int_{A_R} \frac{\Gamma(s) x^{-s}}{(^{-s}e)}\,ds \to 0 \)

I believe this is where the problem lies. As I mentioned, the reciprocal tetrational is going to be unbounded. I believe it is also possible with the topological-transitivity thing I mentioned to show that it will also take on almost every complex value infinitely often, on \( \Re(s) < 0 \). So as the arc \( A_R \) cuts through that highly ill-behaved region, there seems no reason to assume this integral must converge to \( 0 \) as \( R \rightarrow \infty \).