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A069286 Decimal expansion of constant rho satisfying Gaussian Phi(rho * sqrt(2)) = erf(rho) = 1/2. 3

%I #20 Feb 28 2023 04:08:58

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

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

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

%N Decimal expansion of constant rho satisfying Gaussian Phi(rho * sqrt(2)) = erf(rho) = 1/2.

%C In Bronstein-Semendjajew, Gaussian Phi is the probability integral, i.e., 2 * Normal Distribution Function.

%D Bronstein-Semendjajew, Taschenbuch der Mathematik, 7th German ed. 1965, ch. 6.1.2.

%H G. C. Greubel, <a href="/A069286/b069286.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InverseErf.html">Inverse Erf</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/ProbableError.html">Probable Error</a> t= rho * sqrt(2)= 06745...

%e 0.4769362762044698733814183536431305598089697490594706447...

%t RealDigits[ InverseErf[1/2], 10, 105][[1]] (* _Robert G. Wilson v_, Oct 11 2004 *)

%o (PARI) solve(x=0, 1, erfc(x)-1/2) \\ _Charles R Greathouse IV_, Oct 15 2015

%Y Cf. A069287 (continued fraction), A007680.

%K nonn,cons

%O 0,1

%A _Frank Ellermann_, Mar 13 2002

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)