Math help: Calculate pi using Gregory's Series on Beowulf?

Martin Siegert siegert at sfu.ca
Fri Aug 3 19:39:15 EDT 2001


On Fri, Aug 03, 2001 at 07:34:29PM -0400, Robert G. Brown wrote:
> On Fri, 3 Aug 2001, Chris Richard Adams wrote:
> 
> > Thanks, but I don't understand your notation:
> >
> > arctan(x) = int_0^x[dy 1/(1 + y^2)]
> >
> > how is a function of x dependent on y?  I'll look this up, but is this
> 
> An INTEGRAL of y.  With x as an upper limit.  I'm too lazy to actually
> do it, but try either integrating by parts or expanding (1+y^2)^-1 in a
> taylor series and then integrating -- that sort of thing.  There's
> probably a simple trick for converting this into a series.
> 

Try substituting y=tan z. You end up integrating over 1 - even I can do it :-)

Cheers,
Martin

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