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Fungrim entry: 19d7d9

sinc(z)=(2zπ)1/2J1/2 ⁣(z)\operatorname{sinc}(z) = {\left(\frac{2 z}{\pi}\right)}^{-1 / 2} J_{1 / 2}\!\left(z\right)
Assumptions:zC  and  z0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
TeX:
\operatorname{sinc}(z) = {\left(\frac{2 z}{\pi}\right)}^{-1 / 2} J_{1 / 2}\!\left(z\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
Definitions:
Fungrim symbol Notation Short description
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Powab{a}^{b} Power
Piπ\pi The constant pi (3.14...)
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("19d7d9"),
    Formula(Equal(Sinc(z), Mul(Pow(Div(Mul(2, z), Pi), Neg(Div(1, 2))), BesselJ(Div(1, 2), z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotEqual(z, 0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC