OFFSET
0,2
COMMENTS
For Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1) see A078127.
FORMULA
Equals (3*(log(2))^2-2*gamma*log(2))/4, where gamma is Euler gamma constant A001620.
EXAMPLE
0.16029205508788522645507732800087420061716546391...
MAPLE
(3*(log(2))^2-2*gamma*log(2))/4; evalf(%) ; # R. J. Mathar, Jun 10 2024
MATHEMATICA
RealDigits[(3 Log[2]^2 - 2 EulerGamma Log[2])/4, 10, 106][[1]]
PROG
(PARI) sumalt(k=1, (-1)^(k+1)*log(2*k)/(2*k)) \\ Vaclav Kotesovec, Oct 08 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Oct 07 2023
STATUS
approved