# Fungrim entry: a787eb

$\Gamma(z) \Gamma\!\left(z + \frac{1}{2}\right) = {2}^{1 - 2 z} \sqrt{\pi} \Gamma\!\left(2 z\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; 2 z \notin \{0, -1, \ldots\}$
TeX:
\Gamma(z) \Gamma\!\left(z + \frac{1}{2}\right) = {2}^{1 - 2 z} \sqrt{\pi} \Gamma\!\left(2 z\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; 2 z \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
Gamma$\Gamma(z)$ Gamma function
Pow${a}^{b}$ Power
Sqrt$\sqrt{z}$ Principal square root
Pi$\pi$ The constant pi (3.14...)
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("a787eb"),
Formula(Equal(Mul(Gamma(z), Gamma(Add(z, Div(1, 2)))), Mul(Mul(Pow(2, Sub(1, Mul(2, z))), Sqrt(Pi)), Gamma(Mul(2, z))))),
Variables(z),
Assumptions(And(Element(z, CC), NotElement(Mul(2, z), ZZLessEqual(0)))))

## Topics using this entry

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