Fungrim home page

Fungrim entry: ad9caa

z2Jν ⁣(z)+zJν ⁣(z)+(z2ν2)Jν ⁣(z)=0{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:νZandzC\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Alternative assumptions:νCandzC{0}\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
Powab{a}^{b} Power
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ZZZ\mathbb{Z} Integers
CCC\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.

2019-09-15 11:00:55.020619 UTC