Fungrim entry: af4516

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \operatorname{sinc}(z) = \left\{ \pi n : n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0 \right\}

TeX:

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \operatorname{sinc}(z) = \left\{ \pi n : n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \ne 0 \right\}

Definitions:

Fungrim symbol	Notation	Short description
`Zeros`	$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$	Zeros (roots) of function
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`CC`	$\mathbb{C}$	Complex numbers
`Pi`	$\pi$	The constant pi (3.14...)
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("af4516"),
    Formula(Equal(Zeros(Sinc(z), ForElement(z, CC)), Set(Mul(Pi, n), ForElement(n, ZZ), NotEqual(n, 0)))))

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