A242943 - OEIS

%I #7 May 27 2014 10:15:22

%S 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,

%T 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,

%U 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

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

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

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/RenyisParkingConstants.html">Rényi's Parking Constants</a>

%F 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.

%e 0.808652518350212244915421929409680329441...

%t 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

%Y Cf. A050996.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, May 27 2014