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

0,1

Comments

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

Links

Table of n, a(n) for n=0..99.

Eric Weisstein's World of Mathematics, BBP Formula

Formula

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

Example

0.2050025576364235339441503362184922669061652427121494396000185063478...

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]

Prog

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

Crossrefs

Cf. A000796, A145960, A145961, A145963.

Sequence in context: A356815 A352554 A352563 * A066442 A171388 A086134

Adjacent sequences: A145959 A145960 A145961 * A145963 A145964 A145965

Keyword

cons,nonn

Author

Artur Jasinski, Oct 25 2008

Extensions

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

Status

approved