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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's MathWorld, Rényi's Parking Constants

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

Adjacent sequences: A247389 A247390 A247391 * A247393 A247394 A247395

KEYWORD

nonn,cons,more

AUTHOR

Jean-François Alcover, Sep 16 2014

STATUS

approved

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Last modified December 4 19:07 EST 2022. Contains 358563 sequences. (Running on oeis4.)