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{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(z \ne 0 \;\mathbin{\operatorname{or}}\; \nu = 0\right)

TeX:

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

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(z \ne 0 \;\mathbin{\operatorname{or}}\; \nu = 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
`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, CC), Element(z, CC), Or(NotEqual(z, 0), Equal(nu, 0)))))

Topics using this entry

Bessel functions