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Search: id:A133658
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| A133658 |
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Decimal expansion of Sum_{x=integer, -inf < x < inf} (1/sqr(2*pi))*exp(-x^2/2). |
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+0
1
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| 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, 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, 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
(list; cons; graph; listen)
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OFFSET
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1,10
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COMMENT
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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 (rgwv(AT)rgwv.com), Dec 30 2007
See A084304 for cont.frac.(1/tanh(pi^2)) = [1, 186895766, 8, 1, 11, 2, 3, ...] [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 24 2009]
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EXAMPLE
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1.000000005350575982148479362482248...
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MATHEMATICA
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RealDigits[(1 + 2*Sum[ Exp[ -x^2/2], {x, 1, 24, 1}])/Sqrt[2 Pi], 10, 2^7][[1]] - Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 30 2007
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PROGRAM
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Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 24 2009: (Start)
(PARI) default(realprecision, 100); sqrt(2/Pi)*(suminf(k=1, exp(-k^2/2))+.5)
vecextract(eval(Vec(Str( % ))), "^2") \\ (End)
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CROSSREFS
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Sequence in context: A117967 A068116 A019172 this_sequence A071050 A089486 A153386
Adjacent sequences: A133655 A133656 A133657 this_sequence A133659 A133660 A133661
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KEYWORD
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cons,nonn
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AUTHOR
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Martin Raab (raab-martin(AT)gmx.de), Dec 28 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 30 2007
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