Interval of Definition of Power Tower Function

Definition

The power tower function is defined on the closed interval $\closedint {e^{-e} } {e^{1/e} }$.

Also see

• Euler's Number to Power of its Negative
• Euler's Number to Power of its Reciprocal

Historical Note

This result was demonstrated by Leonhard Paul Euler.

It was reported in François Le Lionnais and Jean Brette: Les Nombres Remarquables where it is pointed out that $e^{1/e}$ is, interestingly, greater than $1$.

Sources

• 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,06598803584 \ldots$
• 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): $1 \cdotp 44466 \, 7861 \ldots$