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A164003 Decimal expansion of exp(-Pi^2/2). 1

%I #17 Aug 24 2017 20:02:16

%S 0,0,7,1,9,1,8,8,3,3,5,5,8,2,6,3,6,5,6,0,7,8,0,1,3,6,6,3,9,6,3,7,1,2,

%T 0,2,9,5,5,3,6,2,3,1,8,0,8,1,5,9,7,9,4,7,5,5,8,0,3,7,1,8,1,2,4,1,2,1,

%U 3,1,8,8,6,9,7,5,6,6,5,0,8,9,5,9,6,1,0,7,9,4,3,9,8,6,5,6,6,2,3,3,0

%N Decimal expansion of exp(-Pi^2/2).

%C Arises in connection with the expansion (e i)^(Pi i) = e^(Pi i) * i^(Pi i) = -1 * exp(Pi i log i) = -exp(Pi i * Pi/2 i) = -exp(-Pi^2/2) = -0.00719188335582636560780136639...

%C One has to be careful about branches of multivalued complex functions. By definition (e i)^(Pi i) is exp(Pi i log(e i)) [using any of the branches of log] = exp(Pi i (1 + Pi i/2 + 2 n Pi i)) [ for any integer n ] = - exp(- Pi^2/2 - 2 n Pi^2). There is no imaginary part in any of its branches. If n=0 we get (-1) times the present constant.

%H G. C. Greubel, <a href="/A164003/b164003.txt">Table of n, a(n) for n = 0..5000</a>

%e .0071918833558263656078013663963712029553623180815979475580371...

%t Join[{0,0},RealDigits[Exp[-Pi^2/2],10,120][[1]]] (* _Harvey P. Dale_, Jul 11 2011 *)

%o (PARI) exp(-Pi^2/2) \\ _Charles R Greathouse IV_, Mar 25 2014

%K nonn,cons

%O 0,3

%A _N. J. A. Sloane_, Aug 06 2010, based on postings to the Sequence Fans Mailing List by Alonso Del Arte, _Charles R Greathouse IV_, Sean A. Irvine, Robert Israel and other correspondents.

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Last modified March 29 09:28 EDT 2024. Contains 371268 sequences. (Running on oeis4.)