which pi formula is given in the decimal module documentation?

Mark Dickinson dickinsm at gmail.com
Fri Dec 11 05:43:47 EST 2009


On Dec 11, 10:30 am, Mark Dickinson <dicki... at gmail.com> wrote:
> > It looks like an infinite series with term `t`, where`n` = (2k-1)^2
> > and `d` = d = 4k(4k+2) for k = 1... Does it have a name?
>
> Interesting.  So the general term here is
> 3 * (2k choose k) / (16**k * (2*k+1)),  k >= 0.
>
> I've no idea what its name is or where it comes from, though.  I
> expect Raymond Hettinger would know.

After a cup of coffee, it's much clearer:  this just comes from the
Taylor series for arcsin(x), applied to x = 1/2 to get asin(1/2) = pi/
6.

--
Mark



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