Fungrim entry: f64eef

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

Assumptions:

z \in \mathbb{C}

TeX:

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

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Pi`	$\pi$	The constant pi (3.14...)
`Product`	$\prod_{n} f(n)$	Product
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("f64eef"),
    Formula(Equal(Sinc(Mul(Pi, z)), Product(Parentheses(Sub(1, Div(Pow(z, 2), Pow(n, 2)))), 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