OFFSET
4,1
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
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
FORMULA
e^e^... (e times).
EXAMPLE
2075.96833505806583357...
CROSSREFS
KEYWORD
AUTHOR
Marco Ripà, Feb 17 2022
STATUS
approved