A258086 Decimal expansion of Integral_{0..infinity} exp(-x)/(1-x*exp(-x)) dx.

1, 3, 5, 9, 0, 9, 8, 2, 7, 7, 1, 1, 3, 5, 4, 8, 2, 6, 4, 6, 4, 3, 5, 2, 4, 2, 0, 6, 0, 7, 5, 7, 2, 0, 7, 8, 7, 1, 1, 2, 8, 2, 8, 4, 5, 1, 0, 5, 1, 5, 6, 8, 6, 9, 4, 0, 6, 0, 6, 5, 2, 6, 3, 1, 6, 6, 5, 0, 1, 6, 5, 6, 7, 1, 3, 6, 5, 3, 4, 2, 1, 3, 0, 3, 2, 9, 0, 7, 6, 2, 6, 4, 7, 0, 9, 8, 5, 5, 3, 8, 3, 1, 2

Offset: 1

Author

Jean-François Alcover, May 19 2015

Keywords

• nonn
• cons
• easy

Examples

			1.35909827711354826464352420607572078711282845105156869406...
		

Links

• MathOverflow, Upper bound of the waiting time of a sum process.

Programs

Maple

evalf(Int(exp(-x)/(1-x*exp(-x)),x=0..infinity),120); # Vaclav Kotesovec, May 19 2015

Mathematica

c = NIntegrate[Exp[-x]/(1-x*Exp[-x]), {x, 0, Infinity}, WorkingPrecision -> 103]; RealDigits[c] // First

PARI

default(realprecision,120); sumpos(k=0, k!/(k+1)^(k+1)) \\ Vaclav Kotesovec, May 19 2015

Formula

c = Sum_{i >= 0} i!/(i+1)^(i+1).

Equals Integral_{-exp(-1)..0} (LambertW(x)-LambertW(-1,x))/(1+x)^2 dx. - Gleb Koloskov, Jun 12 2021