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Fungrim entry: 95e561

z2Iν ⁣(z)+zIν ⁣(z)(z2+ν2)Iν ⁣(z)=0{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:νZandzC\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Alternative assumptions:νCandzC{0}\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
Powab{a}^{b} Power
BesselIIν ⁣(z)I_{\nu}\!\left(z\right) Modified Bessel function of the first kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("95e561"),
    Formula(Equal(Sub(Add(Mul(Pow(z, 2), BesselI(nu, z, 2)), Mul(z, BesselI(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))))))

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2019-09-15 11:00:55.020619 UTC