[seqfan] Re: formula for Pi

Hector Zenil hzenilc at gmail.com
Sun Dec 7 16:48:01 CET 2008


Is it possible to get subsequences of the digits of Pi from this
formula? Of course without doing N[formula,digits] or any other
similar trick...


On Sun, Dec 7, 2008 at 3:28 PM, Vladimir Bondarenko <vb at cybertester.com> wrote:
> Hello,
>
> This is an exact formula for Pi.
>
> FullSimplify[6/7*(1/3*Sum[(843*n + 4607)/((n + 5)*(3*n + 7)*(3*n + 22)),
> {n, 0, Infinity}] - 655999/248976 - 7/2*Log[3])*Sqrt[3]]
>
> Pi
>
> Cheers,
>
> Vladimir Bondarenko
>
> Quoting Alexander Povolotsky <apovolot at gmail.com>:
>
>> I've got this very ugly formula by playing Maple syntax via old and
>> new inverse symbolic calculators :
>>
>> Pi = 6/7*(1/3*sum((843*n + 4607)/((n+5)*(3*n+7)*(3*n+22)),n=0...infinity)
>>  - 655999/248976  - 7/2*ln(3))*sqrt(3)
>>
>> What I've got for Pi above - is it just a good approximation or exact ?
>> (My old PC with PARI/GP can not get over the summing )
>>
>> It looks that this 655999/248976 fraction quickly becomes periodic around
>>  920249341301972880
>>
>> gp > \p 1000
>> realprecision = 1001 significant digits (1000 digits displayed)
>> gp > 1.0*655999/248976
>> %4 = 2.6347880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 920249341301972880
>> 92024934130197......
>> 288092....
>>
>> Cheers Alexander R. Povolotsky
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Hector Zenil				http://www.mathrix.org




More information about the SeqFan mailing list