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A042972 Decimal expansion of i^(-i), where i = sqrt(-1). 13
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116.
FORMULA
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
EXAMPLE
4.81047738096535165547303566670383312639017087466453494002...
MAPLE
evalf[110](I^(-I)); # Muniru A Asiru, Feb 17 2019
MATHEMATICA
RealDigits[Re[I^(1/I)], 10, 100][[1]] (* Alonso del Arte, Oct 31 2011 *)
RealDigits[ Exp[Pi/2], 10, 111][[1]] (* Robert G. Wilson v, Apr 08 2014 *)
PROG
(PARI) default(realprecision, 110); exp(Pi/2) \\ Nathaniel Johnston, Apr 15 2011 (modified by G. C. Greubel, Feb 17 2019)
(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
CROSSREFS
Cf. A049006.
Sequence in context: A013328 A143462 A190966 * A021875 A200356 A127734
KEYWORD
cons,nonn
AUTHOR
EXTENSIONS
a(100) corrected by Nathaniel Johnston, Apr 15 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)