0,2

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Rényi Parking Constant, p. 279.

Eric Weisstein's MathWorld, Rényi's Parking Constants

beta(x) = exp(-2*(Gamma(0, x) + log(x) + EulerGamma)), where Gamma(0,x) is the incomplete Gamma function,

m = A050996 = Integral_{x=0..oo} beta(x) dx,

alpha(x) = m - Integral_{t=0..x} beta(t) dt,

v = 4*Integral_{x=0..oo} ((1 - exp(-x))*alpha(x))/(x*exp(x)) - ((x + exp(-x) - 1)*alpha(x)^2)/((beta(x)*x^2)* exp(2*x)) dx - m.

0.0381563991904265053291044982253...

digits = 30; beta[x_] := Exp[-2*(Gamma[0, x] + Log[x] + EulerGamma)]; m = NIntegrate[beta[x], {x, 0, Infinity}, WorkingPrecision -> digits+5]; alpha[x_?NumericQ] := m - NIntegrate[beta[t], {t, 0, x}, WorkingPrecision -> digits+5]; v = 4*NIntegrate[((1 - Exp[-x])*alpha[x])/(x*Exp[x]) - ((x + Exp[-x] - 1)*alpha[x]^2)/((beta[x]*x^2)* Exp[2*x]), {x, 0, Infinity}, WorkingPrecision -> digits+5] - m; Join[{0}, First[RealDigits[v, 10, digits]]]

Cf. A050996.

Sequence in context: A238169 A341414 A086245 * A219995 A021266 A054399

Adjacent sequences: A247389 A247390 A247391 * A247393 A247394 A247395

nonn,cons,more

Jean-François Alcover, Sep 16 2014

approved