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Search: id:A145963
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| A145963 |
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Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] = 1.00718... used by BBP Pi formula |
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+0
4
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| 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; cons; graph; listen)
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OFFSET
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1,4
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COMMENT
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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
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LINKS
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Weisstein, Eric W., BBP Formula.
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MATHEMATICA
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First[RealDigits[Hypergeometric2F1[1, 1/8, 9/8, 1/16], 10, 100]
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CROSSREFS
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A000796, A145960, A145961, A145962
Sequence in context: A021937 A021586 A091131 this_sequence A153625 A011100 A111293
Adjacent sequences: A145960 A145961 A145962 this_sequence A145964 A145965 A145966
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KEYWORD
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cons,nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 25 2008
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