OFFSET
0,1
COMMENTS
If Schanuel's Conjecture is true, then i^e^Pi is transcendental (see Marques and Sondow 2010, p. 79).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
S. Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 1.1
D. Marques and J. Sondow, Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental, https://arxiv.org/abs/1010.6216, 201-2011; East-West J. Math., 12 (2010), 75-84.
Wikipedia, Schanuel's conjecture
EXAMPLE
i^e^Pi = 0.2192048949... - 0.9756788478...*i
MATHEMATICA
RealDigits[Im[I^E^Pi], 10, 100] // First
PROG
(PARI) abs(imag(I^(exp(Pi)))) \\ Michel Marcus, Aug 19 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Aug 28 2011
STATUS
approved