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Fungrim entry: 86bc7d

Iν ⁣(z)=zν(iz)νJν ⁣(iz)I_{\nu}\!\left(z\right) = {z}^{\nu} {\left(i z\right)}^{-\nu} J_{\nu}\!\left(i z\right)
Assumptions:νZ0andzC\nu \in \mathbb{Z}_{\ge 0} \,\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:
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
BesselIIν ⁣(z)I_{\nu}\!\left(z\right) Modified Bessel function of the first kind
Powab{a}^{b} Power
ConstIii Imaginary unit
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\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))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC