# 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...)
Sum$\sum_{n} f\!\left(n\right)$ Sum
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"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-17 11:32:46.829430 UTC