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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:νC  and  zC  and  (z0  or  ν=0)\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(z \ne 0 \;\mathbin{\operatorname{or}}\; \nu = 0\right)
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)
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
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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)))))

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

2021-03-15 19:12:00.328586 UTC