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A242673
Decimal expansion of the unique real solution of the equation Ei(x)-gamma-log(x) = 1, where Ei is the exponential integral function and gamma the Euler-Mascheroni constant.
3
8, 0, 4, 3, 5, 2, 2, 6, 2, 8, 4, 5, 6, 3, 7, 5, 8, 4, 6, 5, 4, 6, 3, 8, 5, 8, 7, 7, 8, 4, 0, 7, 0, 5, 5, 1, 0, 4, 2, 7, 1, 6, 9, 8, 5, 7, 8, 6, 6, 4, 2, 1, 5, 8, 6, 5, 6, 5, 4, 4, 7, 8, 2, 7, 2, 0, 9, 1, 3, 6, 5, 8, 9, 2, 1, 0, 1, 3, 1, 9, 3, 6, 3, 1, 4, 4, 6, 7, 4, 3, 4, 6, 3, 8, 1, 5, 2, 9, 9, 4
OFFSET
0,1
COMMENTS
This constant is an auxiliary constant used in computing the asymptotic probability of success in one of the Secretary problems.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.
LINKS
EXAMPLE
0.804352262845637584654638587784070551...
MATHEMATICA
a = x /. FindRoot[ExpIntegralEi[x] - EulerGamma - Log[x] == 1, {x, 1}, WorkingPrecision -> 105]; RealDigits[a, 10, 100] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved