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Fungrim entry: 906569

k=1n1sin ⁣(kπn)=n2n1\prod_{k=1}^{n - 1} \sin\!\left(\frac{k \pi}{n}\right) = \frac{n}{{2}^{n - 1}}
Assumptions:nZ1n \in \mathbb{Z}_{\ge 1}
\prod_{k=1}^{n - 1} \sin\!\left(\frac{k \pi}{n}\right) = \frac{n}{{2}^{n - 1}}

n \in \mathbb{Z}_{\ge 1}
Fungrim symbol Notation Short description
Productnf(n)\prod_{n} f(n) Product
Sinsin(z)\sin(z) Sine
Piπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(Product(Sin(Div(Mul(k, Pi), n)), For(k, 1, Sub(n, 1))), Div(n, Pow(2, Sub(n, 1))))),
    Assumptions(Element(n, ZZGreaterEqual(1))))

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2021-03-15 19:12:00.328586 UTC