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A277530
Decimal expansion of the ninth derivative of the infinite power tower function x^x^x... at x = 1/2.
10
8, 4, 4, 6, 1, 7, 0, 8, 6, 7, 1, 0, 9, 3, 6, 1, 1, 9, 7, 5, 1, 5, 8, 2, 0, 7, 1, 1, 4, 9, 3, 8, 3, 2, 2, 3, 9, 5, 4, 6, 1, 0, 0, 2, 1, 7, 3, 6, 6, 2, 7, 5, 5, 1, 8, 4, 4, 1, 7, 2, 9, 4, 8, 3, 6, 5, 8, 0, 2, 4, 8, 4, 2, 5, 9, 8, 1, 7, 4, 6, 6, 3, 5, 1, 9, 8, 8, 5, 9, 6, 2, 2, 4, 9, 1, 5, 0, 1, 6, 9, 8, 4, 3, 5, 1
OFFSET
6,1
LINKS
Eric Weisstein's World of Mathematics, Power Tower.
Wikipedia, Tetration.
EXAMPLE
844617.08671093611975158207114938322395461002...
MATHEMATICA
f[x_] := -ProductLog[-Log[x]]/Log[x]; RealDigits[Derivative[9][f][1/2], 10, 120][[1]] (* Amiram Eldar, May 23 2023 *)
KEYWORD
nonn,cons
AUTHOR
Alois P. Heinz, Oct 19 2016
STATUS
approved