Fungrim entry: 95e561

{z}^{2} I''_{\nu}\!\left(z\right) + z I'_{\nu}\!\left(z\right) - \left({z}^{2} + {\nu}^{2}\right) I_{\nu}\!\left(z\right) = 0

Assumptions:

\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}

Alternative assumptions:

\nu \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

{z}^{2} I''_{\nu}\!\left(z\right) + z I'_{\nu}\!\left(z\right) - \left({z}^{2} + {\nu}^{2}\right) I_{\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
`Pow`	${a}^{b}$	Power
`BesselIDerivative`	$I^{(r)}_{\nu}\!\left(z\right)$	Differentiated modified Bessel function of the first kind
`BesselI`	$I_{\nu}\!\left(z\right)$	Modified Bessel function of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("95e561"),
    Formula(Equal(Sub(Add(Mul(Pow(z, 2), BesselIDerivative(nu, z, 2)), Mul(z, BesselIDerivative(nu, z, 1))), Mul(Add(Pow(z, 2), Pow(nu, 2)), BesselI(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

Bessel functions