[seqfan] Re: Another BBP formula for ln(2) ?

Richard Mathar mathar at strw.leidenuniv.nl
Sun Jul 5 13:39:45 CEST 2009

On behalf of the message of

ap> Return-Path: <seqfan-bounces at list.seqfan.eu>
ap> Date: Sat, 4 Jul 2009 19:35:44 -0400
ap> From: Alexander Povolotsky <apovolot at gmail.com>
ap> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
ap> Cc: lagarias at umich.edu, Marc Chamberland <chamberl at ramanujan.math.grinnell.edu>,
ap> 	David H Bailey <dhbailey at lbl.gov>
ap> Subject: [seqfan]  Another BBP formula for ln(2) ?
ap> ...
ap> FYI - I came up with the following exact BBP formula for ln(2)
ap> log(2)=
ap> (230166911/9240 -
ap> - Sum((1/2)^k*
ap> (11/k+10/(k+1)+9/(k+2)+8/(k+3)+7/(k+4)+6/(k+5)-6/(k+7)-7/(k+8)-8/(k+9)-9/(k+10)-10/(k+11)),
ap>  k = 1 .. infinity))/35917
ap> Could it be reduced to already known BBP variants for ln(2) ?
ap> ...

we can say that there is an infinitude of formulas of this type by inserting
x=1/2 into equation what currently is equation (1.26) of 
and then using a partial fraction decomposition.

Richard Mathar

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