# Fungrim entry: 57fcaf

$\frac{1}{\pi} = 12 \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n} \left(6 n\right)! \left(13591409 + 545140134 n\right)}{\left(3 n\right)! {\left(n !\right)}^{3} \cdot {640320}^{3 n + 3 / 2}}$
TeX:
\frac{1}{\pi} = 12 \sum_{n=0}^{\infty} \frac{{\left(-1\right)}^{n} \left(6 n\right)! \left(13591409 + 545140134 n\right)}{\left(3 n\right)! {\left(n !\right)}^{3} \cdot  {640320}^{3 n + 3 / 2}}
Definitions:
Fungrim symbol Notation Short description
Pi$\pi$ The constant pi (3.14...)
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Factorial$n !$ Factorial
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("57fcaf"),
Formula(Equal(Div(1, Pi), Mul(12, Sum(Div(Mul(Mul(Pow(-1, n), Factorial(Mul(6, n))), Add(13591409, Mul(545140134, n))), Mul(Mul(Factorial(Mul(3, n)), Pow(Factorial(n), 3)), Pow(640320, Add(Mul(3, n), Div(3, 2))))), For(n, 0, Infinity))))))

## Topics using this entry

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

2020-08-27 09:56:25.682319 UTC