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A145962 Decimal expansion of 1/5 Hypergeometric2F1[1, 5/8, 13/8, 1/16] = 0.205... used by 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A145962 = 1/5 Hypergeometric2F1[1, 5/8, 13/8, 1/16] =

Sum[(1/16)^n (1/(8n+5)),{n,0,Infinity}] =

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

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=0..99.

Weisstein, Eric W., BBP Formula

MATHEMATICA

k = First[RealDigits[1/5 Hypergeometric2F1[1, 5/8, 13/8, 1/16], 10, 100]]; Prepend[k, 0]

CROSSREFS

A000796, A145960, A145961, A145963

Sequence in context: A055978 A245695 A069025 * A066442 A171388 A086134

Adjacent sequences:  A145959 A145960 A145961 * A145963 A145964 A145965

KEYWORD

cons,nonn

AUTHOR

Artur Jasinski, Oct 25 2008

EXTENSIONS

Removed leading zero, adjusted offset - R. J. Mathar, Feb 05 2009

STATUS

approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)