Fungrim entry: 6a6a09

H^{(1)}_{\nu}\!\left(z\right) = J_{\nu}\!\left(z\right) + i Y_{\nu}\!\left(z\right)

Assumptions:

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

H^{(1)}_{\nu}\!\left(z\right) = J_{\nu}\!\left(z\right) + i Y_{\nu}\!\left(z\right)

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`HankelH1`	$H^{(1)}_{\nu}\!\left(z\right)$	Hankel function of the first kind
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`ConstI`	$i$	Imaginary unit
`BesselY`	$Y_{\nu}\!\left(z\right)$	Bessel function of the second kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("6a6a09"),
    Formula(Equal(HankelH1(nu, z), Add(BesselJ(nu, z), Mul(ConstI, BesselY(nu, z))))),
    Variables(nu, z),
    Assumptions(And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

Bessel functions

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