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A305200
Decimal expansion of the real part of continued exponential of i.
4
5, 7, 6, 4, 1, 2, 7, 2, 3, 0, 3, 1, 4, 3, 5, 2, 8, 3, 1, 4, 8, 2, 8, 9, 2, 3, 9, 8, 8, 7, 0, 6, 8, 4, 7, 6, 2, 7, 8, 0, 9, 9, 0, 1, 1, 2, 2, 2, 1, 6, 8, 2, 8, 0, 5, 6, 6, 2, 6, 5, 7, 4, 1, 1, 9, 3, 2, 8, 5, 3, 4, 4, 4, 1, 4, 2, 4, 7, 1, 9, 9, 4, 5, 2, 0, 5, 2, 8, 7, 1, 0, 4, 3, 9, 0, 4, 4, 8, 7, 5, 8, 9, 5, 9, 8, 8
OFFSET
0,1
REFERENCES
This is the real part of e^(i*e^(i*e^(i...))).
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
FORMULA
Equals Re(i*LambertW(-i)). - Alois P. Heinz, May 27 2018
From Vaclav Kotesovec, Oct 02 2021: (Start)
Root of the equation exp(x*tan(x)) = cos(x)/x.
Equals Im(LambertW(i)). (End)
EXAMPLE
0.576412723031435283148289239887068476278...
MATHEMATICA
RealDigits[Re[I*LambertW[-I]], 10, 120][[1]] (* Harvey P. Dale, Dec 01 2018 *)
RealDigits[x /. FindRoot[E^(x*Tan[x]) == Cos[x]/x, {x, 1/2}, WorkingPrecision -> 120]][[1]] (* Vaclav Kotesovec, Oct 02 2021 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More digits from Alois P. Heinz, May 27 2018
STATUS
approved