Fungrim entry: 729c78

\operatorname{sinc}\!\left(\pi z\right) = \int_{0}^{1} \cos\!\left(\pi z x\right) \, dx

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{sinc}\!\left(\pi z\right) = \int_{0}^{1} \cos\!\left(\pi z x\right) \, 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
`Cos`	$\cos(z)$	Cosine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("729c78"),
    Formula(Equal(Sinc(Mul(Pi, z)), Integral(Cos(Mul(Mul(Pi, z), x)), For(x, 0, 1)))),
    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