OFFSET
0,1
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.
Eric Weisstein's MathWorld, Sultan's Dowry Problem.
Wikipedia, Secretary problem.
FORMULA
Unique zero of 2*x - sqrt(2*Pi)*(1 - x^2)*exp(x^2/2)*(1 + erf(x/sqrt(2))).
EXAMPLE
0.83992367569237268960377697742181556936162069870391285...
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
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 01 2014
STATUS
approved