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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.

%I A246671 #17 Feb 16 2025 08:33:23
%S A246671 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,
%T A246671 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,
%U A246671 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
%N 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.
%D A246671 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
%H A246671 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 45.
%H A246671 L. A. Shepp, <a href="http://stat.wharton.upenn.edu/~shepp/publications/19.pdf">Explicit Solutions to Some Problems of Optimal Stopping.</a>
%H A246671 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SultansDowryProblem.html">Sultan's Dowry Problem.</a>
%H A246671 Wikipedia, <a href="http://en.wikipedia.org/wiki/Secretary_problem">Secretary problem</a>.
%F A246671 Unique zero of 2*x - sqrt(2*Pi)*(1 - x^2)*exp(x^2/2)*(1 + erf(x/sqrt(2))).
%e A246671 0.83992367569237268960377697742181556936162069870391285...
%t A246671 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
%Y A246671 Cf. A246664, A246665, A246667, A246668.
%K A246671 nonn,cons,easy
%O A246671 0,1
%A A246671 _Jean-François Alcover_, Sep 01 2014