Fungrim entry: fddfe6

\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
`ConstPi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	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)))), Tuple(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"))

Fungrim entry: fddfe6

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