[seqfan] Re: Logarithm related identities (generated by me)

[Richard Mathar]

ap> From seqfan-bounces at list.seqfan.eu Tue Dec 16 22:53:56 2008
ap> Date: Tue, 16 Dec 2008 16:51:32 -0500
ap> From: "Alexander Povolotsky" <apovolot at gmail.com>
ap> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
ap> Subject: [seqfan]  Logarithm related identities (generated by me)
ap> 
ap> Recently I came up with following four natural logarithm related identities
ap> (some of them are fairly simple):
ap> 
ap> ln(3) = 1/4*(1+ Sum((1/(9)^(k+1))*(27/(2*k+1)+4/(2*k+2)+1/(2*k+3)), k = 0 ..
ap> infinity) )
ap> ln(2) = 1/4*(3 - sum(1/(n*(n+1)*(2*n+1)), n=1...infinity))
ap> ln(2) = 105*(319/44100 -
ap> sum(1/(2*n*(2*n+1)*(2*n+3)*(2*n+5)*(2*n+7)),n=1...infinity) )

The previous 2 are probably published elsewhere, because they seem to follow
from standard Taylor expansions of (1+x)*log(1+x). I've put an explicit
derivation of related types
into section 1.511.+1 (page 9, 10 at the moment) of my table
http://www.strw.leidenuniv.nl/~mathar/public/mathar20071105.pdf

ap> ln(2) = (319/420 - 3/2*sum(1/(6*n^2+39*n+63),n=1...infinity))
ap> 
ap> I have not seen (yet)  above four being explicitly published elsewhere.
ap> Please let me know if anyone have seen those published already.

Richard Mathar