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A135040 Decimal expansion of the unique root of equation N(-x) = N'(x), where N(x) is a cumulative standard normal distribution function, N'(x) = 1/sqrt( 2*Pi )*exp( -(x^2)/2 ). 1

%I

%S 3,0,2,6,3,0,8,4,0,7,1,1,5,7,2,7,4,0,8,5,2,8,4,5,6,6,3,1,8,4,2,6,8,5,

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

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

%N Decimal expansion of the unique root of equation N(-x) = N'(x), where N(x) is a cumulative standard normal distribution function, N'(x) = 1/sqrt( 2*Pi )*exp( -(x^2)/2 ).

%H G. C. Greubel, <a href="/A135040/b135040.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StandardNormalDistribution.html">Standard Normal Distribution</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NormalDistributionFunction.html">Normal Distribution Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal Distribution</a>

%e c = 0.302630840711572740852845663184268515313557843072275451584922363....

%t FindRoot[ Exp[ -(x^2)/2 ] == Integrate[ Exp[ -(t^2)/2 ], {t, -Infinity, -x} ], {x,0}]

%t RealDigits[x /. FindRoot[E^(-(x^2/2)) == Sqrt[Pi/2]*Erfc[x/Sqrt[2]], {x, 0}, WorkingPrecision -> 105]][[1]] (* _Jean-Fran├žois Alcover_, Nov 08 2012 *)

%K cons,nonn

%O 0,1

%A _Alexander Adamchuk_, Feb 29 2008, Mar 10 2008

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Last modified September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)