A366349 Decimal expansion of the Sum_{k>=1} (-1)^(k+1)*log(2*k)/(2*k).
1, 6, 0, 2, 9, 2, 0, 5, 5, 0, 8, 7, 8, 8, 5, 2, 2, 6, 4, 5, 5, 0, 7, 7, 3, 2, 8, 0, 0, 0, 8, 7, 4, 2, 0, 0, 6, 1, 7, 1, 6, 5, 4, 6, 3, 9, 1, 9, 0, 4, 3, 4, 2, 2, 0, 9, 8, 0, 1, 9, 8, 0, 1, 9, 9, 2, 0, 0, 4, 1, 9, 0, 0, 3, 7, 9, 0, 2, 7, 3, 3, 7, 7, 0, 1, 9, 6, 6, 1, 4, 7, 0, 5, 9, 4, 0, 4, 0, 1, 3, 1, 9, 0, 4, 1, 9
Offset: 0
Examples
0.16029205508788522645507732800087420061716546391...
Programs
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Maple
(3*(log(2))^2-2*gamma*log(2))/4; evalf(%) ; # R. J. Mathar, Jun 10 2024
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Mathematica
RealDigits[(3 Log[2]^2 - 2 EulerGamma Log[2])/4, 10, 106][[1]]
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PARI
sumalt(k=1, (-1)^(k+1)*log(2*k)/(2*k)) \\ Vaclav Kotesovec, Oct 08 2023
Formula
Equals (3*(log(2))^2-2*gamma*log(2))/4, where gamma is Euler gamma constant A001620.
Comments