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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.
0
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
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
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
nonn,cons,easy
AUTHOR
STATUS
approved