Fungrim entry: 906569

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

Assumptions:

n \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
`Product`	$\prod_{n} f(n)$	Product
`Sin`	$\sin(z)$	Sine
`Pi`	$\pi$	The constant pi (3.14...)
`Pow`	${a}^{b}$	Power
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("906569"),
    Formula(Equal(Product(Sin(Div(Mul(k, Pi), 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

Sine

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

2021-03-15 19:12:00.328586 UTC