A145962 Decimal expansion of (1/5)*Hypergeometric2F1[1, 5/8, 13/8, 1/16] used in BBP Pi formula.

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

Offset: 0

Author

Artur Jasinski, Oct 25 2008

Keywords

• cons
• nonn

Comments

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

Examples

			0.2050025576364235339441503362184922669061652427121494396000185063478...
		

Links

• Eric Weisstein's World of Mathematics, BBP Formula

Crossrefs

Cf. A000796, A145960, A145961, A145963.

Programs

Mathematica

RealDigits[1/5 Hypergeometric2F1[1, 5/8, 13/8, 1/16], 10, 100][[1]]
N[Sum[(1/16)^n (1/(8n+5)),{n,0,Infinity}], 100]
N[Sqrt[2](ArcCot[Sqrt[2]] + ArcCoth[Sqrt[2]]) -Pi/4 - ArcCot[3] - Log[5]/2, 100]

PARI

suminf(k=0, (1/16)^k / (8*k+5)) \\ Michel Marcus, Jan 16 2021

Formula

Equals Sum_{k>=0} (1/16)^k / (8*k+5).

Extensions

Leading zero removed, offset adjusted by R. J. Mathar, Feb 05 2009