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Search: id:A145961
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| A145961 |
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Decimal expansion of 2Log[3] - 4ArcCot[2] = 0.342634... used by BBP Pi formula |
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+0
4
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| 3, 4, 2, 6, 3, 4, 1, 4, 1, 3, 3, 2, 9, 9, 4, 9, 1, 7, 9, 3, 3, 4, 6, 5, 5, 4, 8, 0, 0, 0, 1, 9, 3, 8, 0, 1, 1, 8, 0, 8, 3, 2, 8, 9, 8, 5, 0, 1, 0, 1, 7, 8, 4, 8, 2, 2, 5, 6, 5, 6, 3, 1, 2, 3, 9, 4, 1, 9, 7, 1, 2, 9, 7, 7, 4, 2, 5, 1, 1, 1, 2, 5, 4, 4, 8, 3, 0, 3, 7, 3, 6, 8, 7, 9, 1, 2, 6, 0, 7, 3
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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A145961 = 2Log[3] - 4ArcCot[2] =
1/3 Hypergeometric2F1[1, 3/4, 7/4, 1/16] =
Sum[(1/16)^n (1/(4n+3)),{n,0,Infinity}]
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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k=First[RealDigits[2Log[3] - 4ArcCot[2], 10, 100]]; Prepend[k, 0]
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CROSSREFS
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A000796, A145961, A145962, A145963
Sequence in context: A162196 A133620 A154570 this_sequence A082928 A139524 A108127
Adjacent sequences: A145958 A145959 A145960 this_sequence A145962 A145963 A145964
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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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EXTENSIONS
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Removed leading zero, adjusted offset R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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