OFFSET
1,10
COMMENTS
Standard normal distribution taken at all integers x from -infinity to +infinity.
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).
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
See A084304 for cont.frac.(1/tanh(pi^2)) = [1, 186895766, 8, 1, 11, 2, 3, ...] - M. F. Hasler, Oct 24 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
1.000000005350575982148479362482248...
MATHEMATICA
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 *)
PROG
(PARI) default(realprecision, 100); sqrt(2/Pi)*(suminf(k=1, exp(-k^2/2))+.5)
vecextract(eval(Vec(Str( % ))), "^2") \\ M. F. Hasler, Oct 24 2009
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Martin Raab, Dec 28 2007
EXTENSIONS
More terms from Robert G. Wilson v, Dec 30 2007
STATUS
approved