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Fungrim entry: 0479f5

π=72n=11n(eπn1)96n=11n(e2πn1)+24n=11n(e4πn1)\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
Piπ\pi The constant pi (3.14...)
Sumnf(n)\sum_{n} f(n) Sum
Expez{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"))

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2020-08-27 09:56:25.682319 UTC