Fungrim entry: 6c28fa

\operatorname{sinc}\!\left(-\infty\right) = \lim_{x \to -\infty} \operatorname{sinc}\!\left(a i + x\right) = 0

Assumptions:

a \in \mathbb{C}

TeX:

\operatorname{sinc}\!\left(-\infty\right) = \lim_{x \to -\infty} \operatorname{sinc}\!\left(a i + x\right) = 0

a \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`Infinity`	$\infty$	Positive infinity
`RealLimit`	$\lim_{x \to a} f(x)$	Limiting value, real variable
`ConstI`	$i$	Imaginary unit
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("6c28fa"),
    Formula(Equal(Sinc(Neg(Infinity)), RealLimit(Sinc(Add(Mul(a, ConstI), x)), For(x, Neg(Infinity))), 0)),
    Variables(a),
    Assumptions(Element(a, 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