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

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