[seqfan] Re: Another approximation of pi

[Peter Luschny]

Alonso del Arte:
>As far as I know, our own Daniel Forgues is the first to notice that
>sqrt(9.87654321) = 3.1426968... which is about as good an approximation of
>pi as 22/7. For some Sequences of the Day in September, to suggest that a
>keyword:cons sequence ought to be chosen, I put in the number 9.87654321
>purely as a placeholder. To my pleasant surprise, Dan added his observation
>to the September 30 entry.

Well, the problem here is that you did not stop your placeholder at 9.87.
This would have given Daniel the chance to notice a much better
approximation of Pi than 22/7.

Alexander R. Povolotsky:
>Also it might be worth noting that
>7901234568/987654321*123456789=~987654312
>and as a result
>(79.01234568*1.23456789)^1/4
>gives as well
>3.142696798...

Now this gives me the chance to point to my marvelous formula

\pi=
\left({\frac{\Gamma(\gamma)}{\Gamma(2\gamma)\Gamma(1/2-\gamma)}
+\frac{2\Gamma(1-2\gamma)}{\Gamma(1-\gamma)\Gamma(1/2-\gamma)}}\right)^2
\left(\frac{\Gamma(\gamma)\Gamma(1/2 - \gamma/ 2)}{\Gamma(\gamma /2)}\right)^4

which you can see displayed on http://oeis.org/wiki/User:Peter_Luschny

Peter (... sorry, could not resist.)