OFFSET
0,1
COMMENTS
Equals 1/A042972. - Lekraj Beedassy, Sep 02 2005
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
REFERENCES
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.
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.11, p. 449.
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.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 26.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
Leonhard Euler, Letter to Christian Goldbach, Berlin, June 14 1746.
Simon Plouffe, exp(-Pi/2) also i**i to 10000 digits.
H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116.
Eric Weisstein's World of Mathematics, i.
FORMULA
EXAMPLE
0.20787957635076190854695561983497877003387...
MATHEMATICA
RealDigits[Re[N[I^I, 100]]][[1]]
PROG
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Deepak R. N (deepak_rama(AT)bigfoot.com)
STATUS
approved