Fungrim entry: 99ad29

\operatorname{sinc}\!\left(\pi z\right) = \int_{-1 / 2}^{1 / 2} {e}^{2 \pi i z x} \, dx

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{sinc}\!\left(\pi z\right) = \int_{-1 / 2}^{1 / 2} {e}^{2 \pi i z x} \, dx

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Pi`	$\pi$	The constant pi (3.14...)
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("99ad29"),
    Formula(Equal(Sinc(Mul(Pi, z)), Integral(Exp(Mul(Mul(Mul(Mul(2, Pi), ConstI), z), x)), For(x, Neg(Div(1, 2)), Div(1, 2))))),
    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