Definition:Power Tower Function
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Definition
The power tower function is the real function $f: \R \to \R$ defined on the closed interval $\closedint {e^{-e} } {e^{1/e} }$ as:
- $\map f x = x^{x^{x^{x^{x^{\cdot^{\cdot^\cdot} } } } } }$
where the tower of powers tends to infinity.
Also see
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 444 \, 667 \, 861 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 44466 \, 7861 \ldots$