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A145963 Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] = 1.00718... used by BBP Pi formula 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A145963 = Hypergeometric2F1[1, 1/8, 9/8, 1/16] =

Sum[(1/16)^n (1/(8n+1)),{n,0,Infinity}] =

(*Artur Jasinski*) (1/16) (Pi + 2 Sqrt[2] (2 ArcCoth[Sqrt[2]] + ArcTan[2 Sqrt[2]]) + 2 ArcTan[3/4] + 2 Log[5])

BBP Formula on Pi = 4*A145963-(1/2)A145960-(1/2)A145961-A145962 =

(*Artur Jasinski*) =4((1/16) (Pi + 4 ArcTan[1/3] + 4 Sqrt[2] ArcTan[1/Sqrt[2]] + Log[25] - 2 Sqrt[2] Log[2 - Sqrt[2]] + 2 Sqrt[2] Log[2 + Sqrt[2]]))-

(Sqrt[2] ArcCot[Sqrt[2]] + Sqrt[2] ArcCoth[Sqrt[2]] - Log[5]/2 - Pi/4 - ArcCot[3])-

(1/2)(2*Log[5/3])-

(1/2)(2*Log[3]-2 ArcTan[1/2]) =

Pi = 3.1414... = A000796

LINKS

Table of n, a(n) for n=1..100.

Weisstein, Eric W., BBP Formula.

MATHEMATICA

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

CROSSREFS

A000796, A145960, A145961, A145962

Sequence in context: A021586 A091131 A249279 * A199439 A153625 A011100

Adjacent sequences:  A145960 A145961 A145962 * A145964 A145965 A145966

KEYWORD

cons,nonn

AUTHOR

Artur Jasinski, Oct 25 2008

STATUS

approved

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Last modified September 19 23:59 EDT 2019. Contains 327207 sequences. (Running on oeis4.)