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%I #16 Oct 03 2018 21:33:40
%S 1,0,0,0,0,0,0,0,0,5,3,5,0,5,7,5,9,8,2,1,4,8,4,7,9,3,6,2,4,8,2,2,4,8,
%T 0,8,0,5,3,7,0,6,0,6,4,6,9,5,7,4,4,3,1,7,2,6,3,2,7,5,5,0,7,7,6,0,7,7,
%U 4,9,1,9,1,6,2,8,8,5,4,2,3,0,3,6,5,1,9,5,8,7,9,1,1,9,0,9,1,6,8,4,3,7,6,7,9
%N Decimal expansion of Sum_{x=integer, -inf < x < inf} (1/sqrt(2*Pi))*exp(-x^2/2).
%C Standard normal distribution taken at all integers x from -infinity to +infinity.
%C Not only is this constant quite close to 1/tanh(pi^2) (difference is about 1.43*10^-17), but it is even closer if the second term of its continued fraction, 186895766.612113..., is reduced by 1/2 (the difference then decreases to about 10^-34).
%C The continued fraction begins: 1, 186895766, 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 5, 4, 1, 6, 1, 5, 8, 1, 1, 3, 1, 44, 3, 7, 31, 2, 5, 1, 1, 5, 1, 5, 5334, 1, ... - _Robert G. Wilson v_, Dec 30 2007
%C See A084304 for cont.frac.(1/tanh(pi^2)) = [1, 186895766, 8, 1, 11, 2, 3, ...] - _M. F. Hasler_, Oct 24 2009
%H G. C. Greubel, <a href="/A133658/b133658.txt">Table of n, a(n) for n = 1..10000</a>
%e 1.000000005350575982148479362482248...
%t RealDigits[(1 + 2*Sum[ Exp[ -x^2/2], {x, 1, 24, 1}])/Sqrt[2 Pi], 10, 2^7][[1]] (* _Robert G. Wilson v_, Dec 30 2007 *)
%o (PARI) default(realprecision,100); sqrt(2/Pi)*(suminf(k=1,exp(-k^2/2))+.5)
%o vecextract(eval(Vec(Str( % ))),"^2") \\ _M. F. Hasler_, Oct 24 2009
%K cons,nonn
%O 1,10
%A _Martin Raab_, Dec 28 2007
%E More terms from _Robert G. Wilson v_, Dec 30 2007
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