OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 289.
LINKS
Xavier Gourdon, Largest component in random combinatorial structures, Discrete Mathematics 180, 1998, Pages 185-209.
EXAMPLE
0.049469852279228075333485464056253836603725107670028013295315781039...
MATHEMATICA
digits = 96; F[x_] := 1 - Exp[-x]/Sqrt[Pi*x] - Erf[Sqrt[x]]; Clear[f, g];
f[m_] := f[m] = 2 NIntegrate[(1 - (1 - F[x])^-1), {x, 0, m}, WorkingPrecision -> digits + 10]; f[m = 100]; f[m = 2 m]; Print["m = ", m]; While[RealDigits[f[m], 10, digits + 5][[1]] != RealDigits[f[m/2], 10, digits + 5][[1]], m = 2 m; Print["m = ", m]];
g[m_] := g[m] = (8/3) NIntegrate[(1 - (1 - F[x])^-1)*x, {x, 0, m}, WorkingPrecision -> digits + 10]; g[m = 100]; g[m = 2 m]; Print["m = ", m]; While[RealDigits[g[m], 10, digits + 5][[1]] != RealDigits[g[m/2], 10, digits + 5][[1]], m = 2 m; Print["m = ", m]];
Join[{0}, RealDigits[g[m] - f[m]^2, 10, digits][[1]]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Apr 20 2016
STATUS
approved