Fungrim entry: 3bffa9

\left|J_{\nu}\!\left(x\right)\right| \le 1

Assumptions:

\nu \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}

TeX:

\left|J_{\nu}\!\left(x\right)\right| \le 1

\nu \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("3bffa9"),
    Formula(LessEqual(Abs(BesselJ(nu, x)), 1)),
    Variables(nu, x),
    Assumptions(And(Element(nu, ClosedOpenInterval(0, Infinity)), Element(x, RR))))

Topics using this entry

Bessel functions

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