A242943 Decimal expansion of the mean car density associated with Solomon's variation in Renyi's one-dimensional parking problem.

8, 0, 8, 6, 5, 2, 5, 1, 8, 3, 5, 0, 2, 1, 2, 2, 4, 4, 9, 1, 5, 4, 2, 1, 9, 2, 9, 4, 0, 9, 6, 8, 0, 3, 2, 9, 4, 4, 1, 0, 8, 0, 1, 2, 4, 7, 1, 3, 8, 6, 9, 4, 8, 5, 4, 3, 2, 2, 5, 1, 2, 9, 6, 6, 5, 4, 1, 3, 2, 3, 3, 2, 7, 9, 2, 6, 9, 5, 3, 9, 1, 2, 7, 4, 5, 5, 1, 6, 0, 4, 9, 1, 0, 4, 7, 7, 8, 9, 1, 8, 7, 2

Offset: 0

Author

Jean-François Alcover, May 27 2014

Keywords

• nonn
• cons

Examples

			0.808652518350212244915421929409680329441...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 279.

Links

• Eric Weisstein's MathWorld, Rényi's Parking Constants

Crossrefs

Cf. A050996.

Programs

Mathematica

digits = 102; NIntegrate[(2*x + 1)*Exp[-2*(x + Exp[-x] - 1)]*Exp[-2*(-ExpIntegralEi[-x] + Log[x] + EulerGamma)], {x, 0, Infinity}, WorkingPrecision -> digits + 5] // RealDigits[#, 10, digits] & // First

Formula

Integral_{x>=0} (2*x+1)*exp(-2*(x+exp(-x)-1))*exp(-2*(-Ei(-x)+log(x)+gamma)) dx, where Ei is the exponential integral function and gamma the Euler-Mascheroni constant.