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Fungrim entry: 121b21

J1/2 ⁣(z)=(2zπ)1/2sin⁡ ⁣(z)zJ_{1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\sin\!\left(z\right)}{z}
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
J_{1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\sin\!\left(z\right)}{z}

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
Sinsin⁡ ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("121b21"),
    Formula(Equal(BesselJ(Div(1, 2), z), Mul(Pow(Div(Mul(2, z), ConstPi), Div(1, 2)), Div(Sin(z), z)))),
    Variables(z),
    Assumptions(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.

2019-06-18 07:49:59.356594 UTC