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Fungrim entry: fddfe6

π=k=0116k(48k+128k+418k+518k+6)\pi = \sum_{k=0}^{\infty} \frac{1}{{16}^{k}} \left(\frac{4}{8 k + 1} - \frac{2}{8 k + 4} - \frac{1}{8 k + 5} - \frac{1}{8 k + 6}\right)
References:
  • D. H. Bailey and P. B. Borwein and S. Plouffe (1997). On the rapid computation of various polylogarithmic constants. Mathematics of Computation. vol 66, no 218, p. 903–913. DOI:10.1090/S0025-5718-97-00856-9
TeX:
\pi = \sum_{k=0}^{\infty} \frac{1}{{16}^{k}} \left(\frac{4}{8 k + 1} - \frac{2}{8 k + 4} - \frac{1}{8 k + 5} - \frac{1}{8 k + 6}\right)
Definitions:
Fungrim symbol Notation Short description
ConstPiπ\pi The constant pi (3.14...)
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("fddfe6"),
    Formula(Equal(ConstPi, Sum(Mul(Div(1, Pow(16, k)), Sub(Sub(Sub(Div(4, Add(Mul(8, k), 1)), Div(2, Add(Mul(8, k), 4))), Div(1, Add(Mul(8, k), 5))), Div(1, Add(Mul(8, k), 6)))), For(k, 0, Infinity)))),
    References("D. H. Bailey and P. B. Borwein and S. Plouffe (1997). On the rapid computation of various polylogarithmic constants. Mathematics of Computation. vol 66, no 218, p. 903–913. DOI:10.1090/S0025-5718-97-00856-9"))

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2019-10-05 13:11:19.856591 UTC