Fungrim entry: 5d16e5

\left|{\operatorname{sinc}}^{(n)}(x)\right| \le 1

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}

TeX:

\left|{\operatorname{sinc}}^{(n)}(x)\right| \le 1

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`Sinc`	$\operatorname{sinc}(z)$	Sinc function
`RR`	$\mathbb{R}$	Real numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("5d16e5"),
    Formula(LessEqual(Abs(Derivative(Sinc(x), For(x, x, n))), 1)),
    Variables(x, n),
    Assumptions(And(Element(x, RR), Element(n, ZZGreaterEqual(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