Definition:Power Tower Function

Definition
The power tower function is the real function $f: \R \to \R$ defined on the closed interval $\left[{e^{-e} \,.\,.\, e^{1/e} }\right]$ as:


 * $f \left({x}\right) = x^{x^{x^{x^{x^{\cdot^{\cdot^\cdot} } } } } }$

where the tower of powers tends to infinity.

Also see

 * Interval of Definition of Power Tower Function