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A049006
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Decimal expansion of i^i = exp(-Pi/2).
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25
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2, 0, 7, 8, 7, 9, 5, 7, 6, 3, 5, 0, 7, 6, 1, 9, 0, 8, 5, 4, 6, 9, 5, 5, 6, 1, 9, 8, 3, 4, 9, 7, 8, 7, 7, 0, 0, 3, 3, 8, 7, 7, 8, 4, 1, 6, 3, 1, 7, 6, 9, 6, 0, 8, 0, 7, 5, 1, 3, 5, 8, 8, 3, 0, 5, 5, 4, 1, 9, 8, 7, 7, 2, 8, 5, 4, 8, 2, 1, 3, 9, 7, 8, 8, 6, 0, 0, 2, 7, 7, 8, 6, 5, 4, 2, 6, 0, 3, 5
(list;
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refs;
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OFFSET
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0,1
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COMMENTS
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Euler knew this number to be purely real, and called the fact "remarkable" in a letter to Goldbach dated June 14, 1746. - Alonso del Arte, Nov 30 2012
The value follows immediately from Euler's formula i = exp(i Pi/2) and the rule (a^b)^c = a^(b*c). - The value given by Uhler has the final digits ...14 instead ...08, which is compatible with the claimed accuracy of 52 digits. - M. F. Hasler, May 17 2018
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REFERENCES
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Florian Cajori, History of Mathematics. New York: Chelsea Publishing Company for the American Mathematical Society (1991): 236.
Ian Connell, Modern Algebra: A Constructive Introduction. New York: Elsevier (1981) p. 363.
Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 97.
Reinhold Remmert, Theory of Complex Functions: Readings in Mathematics. New York: Springer-Verlag (1991): 162.
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LINKS
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Eric Weisstein's World of Mathematics, i.
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EXAMPLE
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0.20787957635076190854695561983497877003387...
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MATHEMATICA
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RealDigits[Re[N[I^I, 100]]][[1]]
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PROG
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(PARI) { default(realprecision, 20080); x=10*exp(-Pi/2); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b049006.txt", n, " ", d)); } \\ Harry J. Smith, Apr 28 2009, corrected May 19 2009
(PARI) digits(exp(-Pi/2)\.1^default(realprecision))[^-1] \\ 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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Deepak R. N (deepak_rama(AT)bigfoot.com)
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STATUS
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approved
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