A240243 Decimal expansion of Integral_(x=c..infinity) (log(x)/(1+x))^2 dx, where c = A141251 = e^(LambertW(1/e)+1) corresponds to the maximum of the function.
1, 5, 0, 6, 4, 5, 8, 7, 4, 2, 5, 8, 9, 7, 4, 5, 9, 4, 6, 0, 5, 8, 0, 8, 1, 7, 9, 8, 0, 9, 2, 5, 0, 8, 9, 0, 1, 6, 2, 9, 6, 5, 9, 9, 0, 0, 9, 8, 7, 2, 2, 0, 6, 0, 6, 1, 5, 2, 1, 2, 1, 1, 4, 3, 6, 5, 0, 0, 6, 3, 5, 6, 2, 1, 3, 9, 9, 3, 4, 4, 7, 5, 4, 7, 8, 6, 3, 9, 5, 3, 0, 5, 5, 1, 4, 7, 3, 0, 6, 6
Offset: 1
Examples
1.50645874258974594605808179809250890162965990098722060615212114365006356...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Programs
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Mathematica
w = ProductLog[1/E]; w + w^2 + 2 *Log[1+w]*(1+w) - 2*PolyLog[2, -w] // RealDigits[#, 10, 100]& // First
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PARI
(w -> w + w^2 + 2*(1+w)*log(1+w) - 2*polylog(2, -w))(lambertw(exp(-1)))