Fungrim entry: 8ef3d7

\int_{-\infty}^{z} \operatorname{sinc}(x) \, dx = \operatorname{Si}(z) + \frac{\pi}{2}

Assumptions:

z \in \mathbb{C}

TeX:

\int_{-\infty}^{z} \operatorname{sinc}(x) \, dx = \operatorname{Si}(z) + \frac{\pi}{2}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Infinity`	$\infty$	Positive infinity
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("8ef3d7"),
    Formula(Equal(Integral(Sinc(x), For(x, Neg(Infinity), z)), Add(SinIntegral(z), Div(Pi, 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