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Fungrim entry: 54bce2

Jn ⁣(z)=(1)nJn ⁣(z)J_{-n}\!\left(z\right) = {\left(-1\right)}^{n} J_{n}\!\left(z\right)
Assumptions:nZ  and  zCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
J_{-n}\!\left(z\right) = {\left(-1\right)}^{n} J_{n}\!\left(z\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Fungrim symbol Notation Short description
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(BesselJ(Neg(n), z), Mul(Pow(-1, n), BesselJ(n, 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.

2021-03-15 19:12:00.328586 UTC