Complex Generalisation of Infinite Tetration

Algebra Level 4

Tetration is defined as

\[ \large {^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n \]

If \(z\) is a complex number, then find the value of

\[{^{\infty}z}\]

Details and Assumptions:

\(W\) is the Lambert's W function. It is defined as" \(x = W(x) e^{W(x)} \) for all complex number \(x\).

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