

A049006


Decimal expansion of i^i = exp(Pi/2).


22



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
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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: SpringerVerlag (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 digits
H. S. Uhler, On the numerical value of i^i, Amer. Math. Monthly, 28 (1921), 114116.
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=(xd)*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

Cf. A049007, A202501 (tetration).
Cf. A077589 and A077590 for i^i^i^...
Sequence in context: A243444 A256293 A272002 * A211113 A011389 A021485
Adjacent sequences: A049003 A049004 A049005 * A049007 A049008 A049009


KEYWORD

nonn,cons,changed


AUTHOR

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


STATUS

approved



