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A247392
Decimal expansion of 'v', a parking constant associated with the asymptotic variance of the number of cars that can be parked in a given interval.
2
0, 3, 8, 1, 5, 6, 3, 9, 9, 1, 9, 0, 4, 2, 6, 5, 0, 5, 3, 2, 9, 1, 0, 4, 4, 9, 8, 2, 2, 5, 3
OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Rényi Parking Constant, p. 279.
LINKS
FORMULA
beta(x) = exp(-2*(Gamma(0, x) + log(x) + EulerGamma)), where Gamma(0,x) is the incomplete Gamma function,
m = A050996 = integral_{0..infinity} beta(x) dx,
alpha(x) = m - integral_{0..x} beta(t) dt,
v = 4*integral_{0..infinity} (((1 - exp(-x))*alpha(x))/(x*exp(x)) - ((x + exp(-x) - 1)*alpha(x)^2)/((beta(x)*x^2)* exp(2*x)) dx.
EXAMPLE
0.0381563991904265053291044982253...
MATHEMATICA
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]]]
CROSSREFS
Cf. A050996.
Sequence in context: A238169 A341414 A086245 * A219995 A021266 A054399
KEYWORD
nonn,cons,more
AUTHOR
STATUS
approved