Fungrim entry: d38a03

\sin\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(z\right) \Gamma\!\left(1 - z\right)}

Assumptions:

z \in \mathbb{C}

TeX:

\sin\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(z\right) \Gamma\!\left(1 - z\right)}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sin`	$\sin\!\left(z\right)$	Sine
`ConstPi`	$\pi$	The constant pi (3.14...)
`GammaFunction`	$\Gamma\!\left(z\right)$	Gamma function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("d38a03"),
    Formula(Equal(Sin(Mul(ConstPi, z)), Div(ConstPi, Mul(GammaFunction(z), GammaFunction(Sub(1, 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