Fungrim entry: 0fbd15

\sin\!\left(z\right) = \sqrt{\frac{\pi z}{2}} J_{1 / 2}\!\left(z\right)

Assumptions:

z \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
`Sin`	$\sin\!\left(z\right)$	Sine
`Sqrt`	$\sqrt{z}$	Principal square root
`ConstPi`	$\pi$	The constant pi (3.14...)
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`CC`	$\mathbb{C}$	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)))

Topics using this entry

Sine

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