A246671 Decimal expansion of Shepp's constant 'alpha', an optimal stopping constant associated with the case of a zero mean and unit variance distribution function.

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

Offset: 0

Author

Jean-François Alcover, Sep 01 2014

Keywords

• nonn
• cons
• easy

Examples

			0.83992367569237268960377697742181556936162069870391285...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 45.
• L. A. Shepp, Explicit Solutions to Some Problems of Optimal Stopping.
• Eric Weisstein's MathWorld, Sultan's Dowry Problem.
• Wikipedia, Secretary problem.

Crossrefs

Cf. A246664, A246665, A246667, A246668.

Programs

Mathematica

x /. FindRoot[2*x - Sqrt[2*Pi]*(1 - x^2)*Exp[x^2/2]*(1 + Erf[x/Sqrt[2]]) == 0, {x, 1}, WorkingPrecision -> 103] // RealDigits // First

Formula

Unique zero of 2*x - sqrt(2*Pi)*(1 - x^2)*exp(x^2/2)*(1 + erf(x/sqrt(2))).