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Fungrim entry: a2a294

J3/2 ⁣(z)=(2zπ)1/2(sin⁡(z)z2−cos⁡(z)z)J_{3 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \left(\frac{\sin(z)}{{z}^{2}} - \frac{\cos(z)}{z}\right)
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
J_{3 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \left(\frac{\sin(z)}{{z}^{2}} - \frac{\cos(z)}{z}\right)

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
Piπ\pi The constant pi (3.14...)
Sinsin⁡(z)\sin(z) Sine
Coscos⁡(z)\cos(z) Cosine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("a2a294"),
    Formula(Equal(BesselJ(Div(3, 2), z), Mul(Pow(Div(Mul(2, z), Pi), Div(1, 2)), Sub(Div(Sin(z), Pow(z, 2)), Div(Cos(z), z))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2021-03-15 19:12:00.328586 UTC