Fungrim entry: 15bbb1

I_{n}\!\left(z\right) = {i}^{-n} J_{n}\!\left(i z\right)

Assumptions:

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

TeX:

I_{n}\!\left(z\right) = {i}^{-n} J_{n}\!\left(i z\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`BesselI`	$I_{\nu}\!\left(z\right)$	Modified Bessel function of the first kind
`Pow`	${a}^{b}$	Power
`ConstI`	$i$	Imaginary unit
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("15bbb1"),
    Formula(Equal(BesselI(n, z), Mul(Pow(ConstI, Neg(n)), BesselJ(n, Mul(ConstI, 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