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A145963
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Decimal expansion of Hypergeometric2F1[1, 1/8, 9/8, 1/16] used in BBP Pi formula.
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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
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Equals Sum_{k>=0} (1/16)^k / (8*k+1).
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EXAMPLE
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1.00718447641467622864476...
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MATHEMATICA
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First[RealDigits[Hypergeometric2F1[1, 1/8, 9/8, 1/16], 10, 100]]
N[(1/16) (Pi + 2 Sqrt[2] (2 ArcCoth[Sqrt[2]] + ArcTan[2 Sqrt[2]]) + 2 ArcTan[3/4] + 2 Log[5]), 100]
N[Sum[(1/16)^n (1/(8n+1)), {n, 0, Infinity}], 100]
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PROG
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(PARI) suminf(k=0, (1/16)^k / (8*k+1)) \\ Michel Marcus, Jan 16 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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