OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 288.
P. Flajolet and A. M. Odlyzko, Random Mapping Statistics, Advances in Cryptology - EUROCRYPT '89, J.-J. Quisquater and J. Vandewalle (eds.), Lecture Notes in Computer Science, Springer Verlag, 1990, pp. 329-354.
FORMULA
I(x) = integral_(0..x) (exp(-y)/y)*(1 - exp(-2*(y/(exp(x - y) - 1)))) dy,
c = sqrt(Pi/2)*integral_(0..infinity) 1 - exp(Ei(-x) - I(x)) dx, where Ei is the exponential integral function.
EXAMPLE
2.4149010237176162411...
MAPLE
evalf(sqrt(Pi/2)*Int(1 - exp(Ei(-x) - Int((exp(-y)/y)*(1 - exp(-2*(y/(exp(x - y) - 1)))), y=0..x)), x=0..infinity)); # Vaclav Kotesovec, Aug 12 2019
MATHEMATICA
digits = 20; m0 = 100; dm = 10; I0[x_?NumericQ] := NIntegrate[(Exp[-y]/y)*(1 - Exp[-2*(y/(Exp[x - y] - 1))]), {y, 0, x}, WorkingPrecision -> digits+5]; Clear[f]; f[m_] := f[m] = Sqrt[Pi/2]* NIntegrate[1 - Exp[ExpIntegralEi[-x] - I0[x]], {x, 0, m}, WorkingPrecision -> digits+5]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits+5] != RealDigits[f[m - dm], 10, digits+5], Print["m = ", m]; m = m + dm]; RealDigits[f[m], 10, digits] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jun 24 2014
STATUS
approved