Fungrim home page

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}
TeX:
\prod_{k=1}^{n - 1} \sin\!\left(\frac{k \pi}{n}\right) = \frac{n}{{2}^{n - 1}}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
Productnf(n)\prod_{n} f(n) Product
Sinsin(z)\sin(z) Sine
ConstPiπ\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:
Entry(ID("906569"),
    Formula(Equal(Product(Sin(Div(Mul(k, ConstPi), n)), For(k, 1, Sub(n, 1))), Div(n, Pow(2, Sub(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC