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Decimal expansion of imaginary part of the infinite power tower of i.
9

%I #18 Dec 12 2023 22:03:34

%S 3,6,0,5,9,2,4,7,1,8,7,1,3,8,5,4,8,5,9,5,2,9,4,0,5,2,6,9,0,6,0,0,0,6,

%T 5,3,8,2,6,5,7,7,0,3,0,7,8,6,0,2,7,0,0,4,7,4,1,4,5,1,2,9,8,3,8,0,4,6,

%U 0,1,9,5,2,1,1,5,0,7,7,3,0,5,3,2,9,2,2,7,5,4,1,4,0,0,2,5,6,8,6,4,7

%N Decimal expansion of imaginary part of the infinite power tower of i.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/i.html">i</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>

%e 0.36059247187138548595294052690600065382657703078602700474145129838046019521150773...

%p evalf(Im(2*I*LambertW(-I*Pi/2)/Pi), 139); # _Alois P. Heinz_, Dec 12 2023

%t Prepend@@RealDigits[Im[ -ProductLog[ -Log[I]]/Log[I]], 10, 150]

%o (PARI) z=(1+I)/2;e=.1^default(realprecision);until(e>abs(z-z-=(z-I^z)/(1-I^(z+1)*Pi/2)),);digits(imag(z)\e) \\ _M. F. Hasler_, May 17 2018

%Y Cf. A049006, A077589 (real part).

%K nonn,cons,nice

%O 0,1

%A _Eric W. Weisstein_, Nov 07 2002