Fungrim entry: 86bc7d

I_{\nu}\!\left(z\right) = {z}^{\nu} {\left(i z\right)}^{-\nu} J_{\nu}\!\left(i z\right)

Assumptions:

\nu \in \mathbb{Z}_{\ge 0} \,\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:

I_{\nu}\!\left(z\right) = {z}^{\nu} {\left(i z\right)}^{-\nu} J_{\nu}\!\left(i z\right)

\nu \in \mathbb{Z}_{\ge 0} \,\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
`BesselI`	$I_{\nu}\!\left(z\right)$	Modified Bessel function of the first kind
`Pow`	${a}^{b}$	Power
`ConstI`	$i$	Imaginary unit
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("86bc7d"),
    Formula(Equal(BesselI(nu, z), Mul(Mul(Pow(z, nu), Pow(Mul(ConstI, z), Neg(nu))), BesselJ(nu, Mul(ConstI, z))))),
    Variables(nu, z),
    Assumptions(And(Element(nu, ZZGreaterEqual(0)), Element(z, CC)), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

Bessel functions