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Fungrim entry: 15bbb1

In ⁣(z)=inJn ⁣(iz)I_{n}\!\left(z\right) = {i}^{-n} J_{n}\!\left(i z\right)
Assumptions:nZ  and  zCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
I_{n}\!\left(z\right) = {i}^{-n} J_{n}\!\left(i z\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
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
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("15bbb1"),
    Formula(Equal(BesselI(n, z), Mul(Pow(ConstI, Neg(n)), BesselJ(n, Mul(ConstI, z))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, CC))))

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

2020-04-08 16:14:44.404316 UTC