A145963 Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] used in BBP Pi formula.

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, 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, 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

Offset: 1

Author

Artur Jasinski, Oct 25 2008

Keywords

• cons
• nonn

Comments

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

Examples

			1.00718447641467622864476...
		

Links

• Eric Weisstein's World of Mathematics, BBP Formula.

Crossrefs

Cf. A000796, A145960, A145961, A145962.

Programs

Mathematica

First[RealDigits[Hypergeometric2F1[1, 1/8, 9/8, 1/16], 10, 100]]
N[(1/16) (Pi + 2 Sqrt[2] (2 ArcCoth[Sqrt[2]] + ArcTan[2 Sqrt[2]]) + 2 ArcTan[3/4] + 2 Log[5]), 100]
N[Sum[(1/16)^n (1/(8n+1)),{n,0,Infinity}], 100]

PARI

suminf(k=0, (1/16)^k / (8*k+1)) \\ Michel Marcus, Jan 16 2021

Formula

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