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

[Alexander Povolotsky]

>The previous 2 are probably published elsewhere

When you will find exact sources of publishing (if they indeed do exist)
please kindly let me know. Then, of course, I will relinquish my claim of
authorship for those.

Regards,
Alexander R. Povolotsky

On Wed, Dec 17, 2008 at 8:33 AM, Richard Mathar
<mathar at strw.leidenuniv.nl>wrote:

>
> 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<http://www.strw.leidenuniv.nl/%7Emathar/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
>
>
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