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A042972
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Decimal expansion of i^(-i), where i = sqrt(-1).
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13
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4, 8, 1, 0, 4, 7, 7, 3, 8, 0, 9, 6, 5, 3, 5, 1, 6, 5, 5, 4, 7, 3, 0, 3, 5, 6, 6, 6, 7, 0, 3, 8, 3, 3, 1, 2, 6, 3, 9, 0, 1, 7, 0, 8, 7, 4, 6, 6, 4, 5, 3, 4, 9, 4, 0, 0, 2, 0, 8, 1, 5, 4, 8, 9, 2, 4, 2, 5, 5, 1, 9, 0, 4, 8, 9, 1, 5, 8, 2, 1, 3, 6, 7, 4, 8, 7, 0, 4, 7, 6, 6, 5, 8, 3, 8, 8, 3, 3, 5, 4
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OFFSET
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1,1
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COMMENTS
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Square root of Gelfond's constant (A039661). Since Gelfond's constant e^Pi is transcendental, e^(Pi/2) is transcendental. - Daniel Forgues, Apr 15 2011
The complex sequence (...((((i)^i)^i)^i)^...) (n pairs of brackets) is periodic with period 4 and the first four entries are i, e^(-Pi/2), -i, e^(+Pi/2). See A049006 for e^(-Pi/2). - Wolfdieter Lang, Apr 27 2013
A solution of x^i + x^(-i) = 0. In fact, x = Exp(Pi/2 + k*Pi), where k is any integer. - Robert G. Wilson v, Feb 04 2014
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LINKS
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FORMULA
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Equals i^(-i) = i^(1/i) = e^(Pi/2).
Also (((i)^i)^i)^i. See a comment above on such powers. - Wolfdieter Lang, Apr 27 2013
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EXAMPLE
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4.81047738096535165547303566670383312639017087466453494002...
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MAPLE
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MATHEMATICA
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PROG
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(Magma) SetDefaultRealField(RealField(110)); R:= RealField(); Exp(Pi(R)/2); // G. C. Greubel, Feb 17 2019
(Sage) numerical_approx(exp(pi/2), digits=110) # G. C. Greubel, Feb 17 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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