Fungrim entry: 24c17b

\operatorname{sinc}(z) = \prod_{n=1}^{\infty} \cos\!\left(\frac{z}{{2}^{n}}\right)

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{sinc}(z) = \prod_{n=1}^{\infty} \cos\!\left(\frac{z}{{2}^{n}}\right)

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Product`	$\prod_{n} f(n)$	Product
`Cos`	$\cos(z)$	Cosine
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("24c17b"),
    Formula(Equal(Sinc(z), Product(Cos(Div(z, Pow(2, n))), For(n, 1, Infinity)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Sinc function

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