|
%I #22 Sep 30 2022 23:51:18
%S 7,6,3,9,4,3,7,2,6,8,4,1,0,9,7,6,1,1,6,9,0,6,4,2,0,6,4,1,8,8,0,6,8,9,
%T 3,7,7,6,5,4,0,6,2,9,9,5,5,4,1,9,0,9,5,3,9,8,8,8,0,3,2,5,1,4,8,2,7,0,
%U 4,6,2,8,6,4,4,2,8,7,3,6,8,4,3,2,5,4,6,2,5,3,2,7,8,0,1,4,8,1,2,5,8,9,1,4,9
%N Decimal expansion of 24/Pi.
%H G. C. Greubel, <a href="/A132714/b132714.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F 24/Pi = Sum_{k>=0} ( (30*k+7)*C(2*k,k)^2*(Hypergeometric2F1[1/2 - k/2, -k/2, 1, 64])/(-256)^k ). - _Alexander R. Povolotsky_, Dec 20 2012
%F Another version of this identity is: Sum[(30*k+7) * Binomial[2k,k]^2 * (Sum[Binomial[k-m,m] * Binomial[k,m] * 16^m, {m,0,k/2}])/(256)^k, {k,0,infinity}]. - _Alexander R. Povolotsky_, Jan 25 2013
%e =7.639437268410976116906420641880689377654062995541909539888032514827...
%t RealDigits[N[24/Pi,6! ]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 03 2009 *)
%o (PARI) 24/Pi \\ _G. C. Greubel_, Feb 20 2017
%Y Cf. A049541, A060294, A089491, A088538, A086201, A132696 to A132699, A132701, A132702.
%K cons,easy,nonn
%O 1,1
%A _Omar E. Pol_, Aug 31 2007
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 03 2009
|
