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
`BesselYDerivative`	$Y^{(r)}_{\nu}\!\left(z\right)$	Differentiated Bessel function of the second kind
`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), BesselYDerivative(nu, z, 2)), Mul(z, BesselYDerivative(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

Bessel functions