Fungrim entry: b7a578

\cos\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}

Assumptions:

z \in \mathbb{C}

TeX:

\cos\!\left(\pi z\right) = \frac{\pi}{\Gamma\!\left(\frac{1}{2} + z\right) \Gamma\!\left(\frac{1}{2} - z\right)}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Cos`	$\cos(z)$	Cosine
`Pi`	$\pi$	The constant pi (3.14...)
`Gamma`	$\Gamma(z)$	Gamma function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("b7a578"),
    Formula(Equal(Cos(Mul(Pi, z)), Div(Pi, Mul(Gamma(Add(Div(1, 2), z)), Gamma(Sub(Div(1, 2), z)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Gamma function

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

2021-03-15 19:12:00.328586 UTC