A346962 Decimal expansion of Integral_{x=-1/e..0} LambertW(x)/LambertW(-1,x) dx.
0, 5, 5, 6, 2, 9, 5, 8, 9, 7, 2, 8, 9, 8, 6, 8, 9, 5, 4, 6, 1, 2, 9, 0, 1, 4, 6, 6, 9, 4, 1, 0, 5, 0, 6, 8, 4, 5, 6, 1, 2, 9, 4, 8, 6, 9, 1, 1, 7, 2, 5, 2, 1, 6, 9, 3, 4, 9, 3, 9, 8, 6, 9, 5, 7, 1, 2, 4, 2, 9, 0, 3, 0, 3, 2, 6, 9, 0, 1, 3, 5, 0, 4, 0, 1, 6, 9, 4, 6, 7, 8, 3, 0, 9, 9, 7, 5, 6, 6, 2, 9, 6, 3, 1, 1, 1, 4, 3
Offset: 0
Examples
0.0556295897289868954612901466941050684561294869117252169349398695712429...
Programs
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Maple
evalf(Integrate(LambertW(x)/LambertW(-1, x), x = -exp(-1)..0), 120); # Vaclav Kotesovec, Aug 23 2021
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Mathematica
N[Integrate[LambertW[x]/LambertW[-1,x],{x,-1/E,0}],120] -
PARI
exp(-1)+intnum(x=0,1,log(x)*x^(1/(1-x))/(1-x))