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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.

%I A351727 #36 Aug 11 2025 07:28:58
%S A351727 2,0,7,5,9,6,8,3,3,5,0,5,8,0,6,5,8,3,3,5,7
%N 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.
%C A351727 Tetration can be extended to complex bases as described in the Paulsen reference.
%C A351727 As far as we know, it has not been proved if e^^e is an irrational number (or not).
%C A351727 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 A351727 Hellmuth Kneser, <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0187">Reelle analytische Lösungen der Gleichung phi(phi(x)) = e^x und verwandter Funktionalgleichungen</a>, J. reine angew. Math. 187, 56-67 (1950)
%H A351727 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 A351727 William Paulsen, <a href="http://myweb.astate.edu/wpaulsen/tetration.html">Tetration</a>.
%H A351727 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 A351727 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F A351727 e^e^... (e times).
%e A351727 2075.96833505806583357...
%Y A351727 Cf. A001113.
%K A351727 nonn,cons,more,hard
%O A351727 4,1
%A A351727 _Marco Ripà_, Feb 17 2022