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Fungrim entry: 6a6a09

Hν(1) ⁣(z)=Jν ⁣(z)+iYν ⁣(z)H^{(1)}_{\nu}\!\left(z\right) = J_{\nu}\!\left(z\right) + i Y_{\nu}\!\left(z\right)
Assumptions:νC  and  zC{0}\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
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\}
Fungrim symbol Notation Short description
HankelH1Hν(1) ⁣(z)H^{(1)}_{\nu}\!\left(z\right) Hankel function of the first kind
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ConstIii Imaginary unit
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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))))))

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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