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A077589
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Decimal expansion of real part of the infinite power tower of i.
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9
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4, 3, 8, 2, 8, 2, 9, 3, 6, 7, 2, 7, 0, 3, 2, 1, 1, 1, 6, 2, 6, 9, 7, 5, 1, 6, 3, 5, 5, 1, 2, 6, 4, 8, 2, 4, 2, 6, 7, 8, 9, 7, 3, 5, 1, 6, 4, 6, 3, 9, 4, 6, 0, 3, 6, 0, 9, 2, 2, 1, 2, 4, 0, 4, 9, 5, 7, 9, 1, 5, 3, 2, 2, 2, 2, 6, 9, 5, 6, 8, 7, 6, 6, 9, 1, 7, 2, 1, 4, 0, 5, 3, 8, 2, 0, 4, 0, 7, 5, 4, 9
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OFFSET
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0,1
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COMMENTS
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This is the real part of i^i^i^i^i^i...
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LINKS
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Eric Weisstein's World of Mathematics, i
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FORMULA
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The value is 2 (i/Pi) W(-i Pi/2) = 0.4382829... + i 0.360592..., where W denotes the principal branch of the Lambert W function. - David W. Cantrell, Nov 23 2007
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EXAMPLE
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0.43828293672703211162697516355126482426789735164639460360922124049579153222269568...
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MAPLE
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evalf(Re(2*I*LambertW(-I*Pi/2)/Pi), 137); # Alois P. Heinz, Dec 12 2023
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MATHEMATICA
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Prepend@@RealDigits[Re[ -ProductLog[ -Log[I]]/Log[I]], 10, 150]
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PROG
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(PARI) z=(1+I)/2; e=.1^default(realprecision); until(e>abs(z-z-=(z-I^z)/(1-I^(z+1)*Pi/2)), ); digits(real(z)\e) \\ M. F. Hasler, May 17 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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