${z}^{2} J''_{\nu}\!\left(z\right) + z J'_{\nu}\!\left(z\right) + \left({z}^{2} - {\nu}^{2}\right) J_{\nu}\!\left(z\right) = 0$
Assumptions:$\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}$
Alternative assumptions:$\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}$
TeX:
{z}^{2} J''_{\nu}\!\left(z\right) + z J'_{\nu}\!\left(z\right) + \left({z}^{2} - {\nu}^{2}\right) J_{\nu}\!\left(z\right) = 0

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

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
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("ad9caa"),
Formula(Equal(Add(Add(Mul(Pow(z, 2), BesselJ(nu, z, 2)), Mul(z, BesselJ(nu, z, 1))), Mul(Sub(Pow(z, 2), Pow(nu, 2)), BesselJ(nu, z))), 0)),
Variables(nu, z),
Assumptions(And(Element(nu, ZZ), Element(z, CC)), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))))))

## Topics using this entry

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