A145963 - OEIS

%I #21 Jan 17 2021 03:13:40

%S 1,0,0,7,1,8,4,4,7,6,4,1,4,6,7,6,2,2,8,6,4,4,7,6,0,1,4,7,4,5,0,4,3,8,

%T 4,9,6,6,4,2,9,6,5,4,7,1,9,4,5,8,8,3,1,1,3,7,1,6,4,3,6,2,0,3,1,7,2,3,

%U 5,2,3,9,0,3,8,0,8,9,8,1,6,3,5,2,7,8,6,8,9,4,4,2,8,9,5,8,5,9,4,9

%N Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] used in BBP Pi formula.

%C BBP formula for Pi = 4*A145963 - (1/2)*A145960 - (1/2)*A145961 - A145962.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BBPFormula.html">BBP Formula</a>.

%F Equals Sum_{k>=0} (1/16)^k / (8*k+1).

%e 1.00718447641467622864476...

%t First[RealDigits[Hypergeometric2F1[1, 1/8, 9/8, 1/16], 10, 100]]

%t N[(1/16) (Pi + 2 Sqrt[2] (2 ArcCoth[Sqrt[2]] + ArcTan[2 Sqrt[2]]) + 2 ArcTan[3/4] + 2 Log[5]), 100]

%t N[Sum[(1/16)^n (1/(8n+1)),{n,0,Infinity}], 100]

%o (PARI) suminf(k=0, (1/16)^k / (8*k+1)) \\ _Michel Marcus_, Jan 16 2021

%Y Cf. A000796, A145960, A145961, A145962.

%K cons,nonn

%O 1,4

%A _Artur Jasinski_, Oct 25 2008