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Fungrim entry: 0fbd15

sin ⁣(z)=πz2J1/2 ⁣(z)\sin\!\left(z\right) = \sqrt{\frac{\pi z}{2}} J_{1 / 2}\!\left(z\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\sin\!\left(z\right) = \sqrt{\frac{\pi z}{2}} J_{1 / 2}\!\left(z\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin ⁣(z)\sin\!\left(z\right) Sine
Sqrtz\sqrt{z} Principal square root
ConstPiπ\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("0fbd15"),
    Formula(Equal(Sin(z), Mul(Sqrt(Div(Mul(ConstPi, z), 2)), BesselJ(Div(1, 2), z)))),
    Variables(z),
    Assumptions(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.

2019-08-21 11:44:15.926409 UTC