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Fungrim entry: 62f23c

z2Yν′′ ⁣(z)+zYν′ ⁣(z)+(z2−ν2)Yν ⁣(z)=0{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:ν∈C  and⁡  z∈C∖{0}\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
Powab{a}^{b} Power
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
CCC\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))))))

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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