Fungrim entry: 0479f5

\pi = 72 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{\pi n} - 1\right)} - 96 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{2 \pi n} - 1\right)} + 24 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{4 \pi n} - 1\right)}

References:

http://www.lacim.uqam.ca/~plouffe/inspired2.pdf

TeX:

\pi = 72 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{\pi n} - 1\right)} - 96 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{2 \pi n} - 1\right)} + 24 \sum_{n=1}^{\infty} \frac{1}{n \left({e}^{4 \pi n} - 1\right)}

Definitions:

Fungrim symbol	Notation	Short description
`Pi`	$\pi$	The constant pi (3.14...)
`Sum`	$\sum_{n} f(n)$	Sum
`Exp`	${e}^{z}$	Exponential function
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0479f5"),
    Formula(Equal(Pi, Add(Sub(Mul(72, Sum(Div(1, Mul(n, Sub(Exp(Mul(Pi, n)), 1))), For(n, 1, Infinity))), Mul(96, Sum(Div(1, Mul(n, Sub(Exp(Mul(Mul(2, Pi), n)), 1))), For(n, 1, Infinity)))), Mul(24, Sum(Div(1, Mul(n, Sub(Exp(Mul(Mul(4, Pi), n)), 1))), For(n, 1, Infinity)))))),
    References("http://www.lacim.uqam.ca/~plouffe/inspired2.pdf"))

Fungrim entry: 0479f5

Topics using this entry