# Fungrim entry: 62f23c

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

\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
BesselY$Y_{\nu}\!\left(z\right)$ Bessel function of the second kind
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("62f23c"),
Formula(Equal(Add(Add(Mul(Pow(z, 2), BesselY(nu, z, 2)), Mul(z, BesselY(nu, z, 1))), Mul(Sub(Pow(z, 2), Pow(nu, 2)), BesselY(nu, z))), 0)),
Variables(nu, z),
Assumptions(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.

2020-04-08 16:14:44.404316 UTC