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.
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