login
A145962
Decimal expansion of (1/5)*Hypergeometric2F1[1, 5/8, 13/8, 1/16] used in BBP Pi formula.
4
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
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
KEYWORD
cons,nonn
AUTHOR
Artur Jasinski, Oct 25 2008
EXTENSIONS
Leading zero removed, offset adjusted by R. J. Mathar, Feb 05 2009
STATUS
approved