A351727 - OEIS

%I #34 Apr 05 2022 08:25:30

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

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

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

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

%C 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

%H Hellmuth Kneser, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002175851">Reelle analytische Lösungen der Gleichung phi(phi(x)) = e^x und verwandter Funktionalgleichungen</a>, J. reine angew. Math. 187, 56-67 (1950)

%H Sheldon Levenstein (user sheldonison), <a href="https://math.eretrandre.org/tetrationforum/showthread.php?tid=1017">New fatou.gp program</a>, Jul 10 2015, updated Aug 14 2019.

%H William Paulsen, <a href="http://myweb.astate.edu/wpaulsen/tetration.html">Tetration</a>.

%H William Paulsen, <a href="https://doi.org/10.1007/s10444-018-9615-7">Tetration for complex bases</a>, Advances in Computational Mathematics, Vol. 45, No. 1 (2019), pp. 243-267; <a href="https://www.researchgate.net/profile/William-Paulsen-2/publication/325532999_Tetration_for_complex_bases/links/5d88c9d992851ceb79346b5f/">ResearchGate link</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>

%F e^e^... (e times).

%e 2075.96833505806583357...

%Y Cf. A001113.

%K nonn,cons,more,hard

%O 4,1

%A _Marco Ripà_, Feb 17 2022