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.

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

Author

Jean-François Alcover, May 20 2014

Keywords

• nonn
• cons

Comments

This constant is an auxiliary constant used in computing the asymptotic probability of success in one of the Secretary problems.

Examples

			0.804352262845637584654638587784070551...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.

Links

• Eric Weisstein's MathWorld, Sultan's Dowry Problem.
• Wikipedia, Secretary problem.

Crossrefs

Cf. A054404, A242672, A242674.

Programs

Mathematica

a = x /. FindRoot[ExpIntegralEi[x] - EulerGamma - Log[x] == 1, {x, 1}, WorkingPrecision -> 105]; RealDigits[a, 10, 100] // First