Fungrim entry: 0836b4

\left|J_{n}\!\left(z\right)\right| \le {e}^{\left|\operatorname{Im}(z)\right|}

Assumptions:

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

TeX:

\left|J_{n}\!\left(z\right)\right| \le {e}^{\left|\operatorname{Im}(z)\right|}

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Abs`	$\left\|z\right\|$	Absolute value
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`Exp`	${e}^{z}$	Exponential function
`Im`	$\operatorname{Im}(z)$	Imaginary part
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("0836b4"),
    Formula(LessEqual(Abs(BesselJ(n, z)), Exp(Abs(Im(z))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, CC))))

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