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

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, 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, 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

Offset: 0

Author

Frank Ellermann, Mar 13 2002

Keywords

• nonn
• cons

Comments

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

Examples

			0.4769362762044698733814183536431305598089697490594706447...
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Inverse Erf.
• Eric Weisstein's World of Mathematics, Normal Distribution Function.
• Eric Weisstein's World of Mathematics, Probable Error t= rho * sqrt(2)= 06745...

Crossrefs

Cf. A069287 (continued fraction), A007680.

Programs

Mathematica

RealDigits[ InverseErf[1/2], 10, 105][[1]] (* Robert G. Wilson v, Oct 11 2004 *)

PARI

solve(x=0, 1, erfc(x)-1/2) \\ Charles R Greathouse IV, Oct 15 2015