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Fungrim entry: 57fcaf

1π=12n=0(1)n(6n)!(13591409+545140134n)(3n)!(n!)36403203n+3/2\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
Piπ\pi The constant pi (3.14...)
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!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))))))

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2020-08-27 09:56:25.682319 UTC