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A049006 Decimal expansion of i^i = exp(-Pi/2). 15
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; constant; graph; refs; listen; history; text; internal format)
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

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.

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 2000 digits

Simon Plouffe, exp(-Pi/2) also i**i to 10000 dogits

S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114-116.

Eric Weisstein's World of Mathematics, i.

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

CROSSREFS

Cf. A049007, A202501 (tetration).

Sequence in context: A243444 A256293 A272002 * A211113 A011389 A021485

Adjacent sequences:  A049003 A049004 A049005 * A049007 A049008 A049009

KEYWORD

nonn,cons

AUTHOR

Deepak R. N (deepak_rama(AT)bigfoot.com)

STATUS

approved

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Last modified June 26 02:24 EDT 2017. Contains 288749 sequences.