${z}^{2} K''_{\nu}\!\left(z\right) + z K'_{\nu}\!\left(z\right) - \left({z}^{2} + {\nu}^{2}\right) K_{\nu}\!\left(z\right) = 0$
Assumptions:$\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}$
TeX:
{z}^{2} K''_{\nu}\!\left(z\right) + z K'_{\nu}\!\left(z\right) - \left({z}^{2} + {\nu}^{2}\right) K_{\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
BesselK$K_{\nu}\!\left(z\right)$ Modified Bessel function of the second kind
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("fd9add"),
Formula(Equal(Sub(Add(Mul(Pow(z, 2), BesselK(nu, z, 2)), Mul(z, BesselK(nu, z, 1))), Mul(Add(Pow(z, 2), Pow(nu, 2)), BesselK(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.

2021-03-15 19:12:00.328586 UTC