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A242943
Decimal expansion of the mean car density associated with Solomon's variation in Renyi's one-dimensional parking problem.
2
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
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 279.
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.
EXAMPLE
0.808652518350212244915421929409680329441...
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
CROSSREFS
Cf. A050996.
Sequence in context: A156744 A228438 A021557 * A358941 A319215 A200513
KEYWORD
nonn,cons
AUTHOR
STATUS
approved