Fungrim entry: b510b6

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

Assumptions:

z \in \mathbb{C} \setminus \mathbb{Z}

TeX:

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

z \in \mathbb{C} \setminus \mathbb{Z}

Definitions:

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

Source code for this entry:

Entry(ID("b510b6"),
    Formula(Equal(GammaFunction(z), Mul(Div(ConstPi, Sin(Mul(ConstPi, z))), Div(1, GammaFunction(Sub(1, z)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, ZZ))))

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.

2019-06-18 07:49:59.356594 UTC