A351727 Decimal expansion of e^^e (tetration of the base e = 2.718281828... of height e), using H. Kneser's proposal for a tetration function.

2, 0, 7, 5, 9, 6, 8, 3, 3, 5, 0, 5, 8, 0, 6, 5, 8, 3, 3, 5, 7

Offset: 4

Author

Marco Ripà, Feb 17 2022

Keywords

• nonn
• cons
• more
• hard

Comments

Tetration can be extended to complex bases as described in the Paulsen reference.

As far as we know, it has not been proved if e^^e is an irrational number (or not).

A conjectured more accurate value of e^^e is 2075.968335058065833574392795134533608218230677029314\ 707635083348823037593106577919477912677373356093134821... obtained with S. Levenstein's PARI program fatou.gp, but its accuracy needs an independent assessment. - Hugo Pfoertner, Feb 22 2022

Examples

			2075.96833505806583357...
		

Links

• Hellmuth Kneser, Reelle analytische Lösungen der Gleichung phi(phi(x)) = e^x und verwandter Funktionalgleichungen, J. reine angew. Math. 187, 56-67 (1950)
• Sheldon Levenstein (user sheldonison), New fatou.gp program, Jul 10 2015, updated Aug 14 2019.
• William Paulsen, Tetration.
• William Paulsen, Tetration for complex bases, Advances in Computational Mathematics, Vol. 45, No. 1 (2019), pp. 243-267; ResearchGate link.
• Wikipedia, Tetration

Crossrefs

Cf. A001113.

Formula

e^e^... (e times).