[seqfan] Re: Logarithm related identities

[Jaume Oliver i Lafont]

> Message: 5
> Date: Tue, 16 Dec 2008 16:51:32 -0500
> From: "Alexander Povolotsky" <apovolot at gmail.com>
> Subject: [seqfan]  Logarithm related identities (generated by me)
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Cc: Florentin Smarandache <fsmarandache at yahoo.com>, Jes?s Guillera
>        <jguillera at gmail.com>
> Message-ID:
>        <144987c90812161351t5c0db0f0taaa96057348ff6c5 at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> 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) )

A similar identity in base 4 is as follows:

ln(3) = 4/3 - (2/3)sum(1/((2k+1)(2k+3)(4^k)),k=0..infinity)

Regards,
Jaume