[seqfan] Logarithm related identities (generated by me)

[Alexander Povolotsky]

Hi,

Just FYI

Recently I came up with following four natural logarithm related identities
(some of them are fairly simple):

ln(3) = 1/4*(1+ Sum((1/(9)^(k+1))*(27/(2*k+1)+4/(2*k+2)+1/(2*k+3)), k = 0 ..
infinity) )
ln(2) = 1/4*(3 - sum(1/(n*(n+1)*(2*n+1)), n=1...infinity))
ln(2) = 105*(319/44100 -
sum(1/(2*n*(2*n+1)*(2*n+3)*(2*n+5)*(2*n+7)),n=1...infinity) )
ln(2) = (319/420 - 3/2*sum(1/(6*n^2+39*n+63),n=1...infinity))

I have not seen (yet)  above four being explicitly published elsewhere.
Please let me know if anyone have seen those published already.

Thanks,
Best Regards,
Alexander R. Povolotsky