Fungrim entry: 19d7d9

\operatorname{sinc}(z) = {\left(\frac{2 z}{\pi}\right)}^{-1 / 2} J_{1 / 2}\!\left(z\right)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0

TeX:

\operatorname{sinc}(z) = {\left(\frac{2 z}{\pi}\right)}^{-1 / 2} J_{1 / 2}\!\left(z\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0

Definitions:

Fungrim symbol	Notation	Short description
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("19d7d9"),
    Formula(Equal(Sinc(z), Mul(Pow(Div(Mul(2, z), Pi), Neg(Div(1, 2))), BesselJ(Div(1, 2), z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotEqual(z, 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