# Fungrim entry: c733f7

$\left(z\right)_{k} = \frac{\Gamma\!\left(z + k\right)}{\Gamma(z)}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z + k \notin \{0, -1, \ldots\}$
TeX:
\left(z\right)_{k} = \frac{\Gamma\!\left(z + k\right)}{\Gamma(z)}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z + k \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
RisingFactorial$\left(z\right)_{k}$ Rising factorial
Gamma$\Gamma(z)$ Gamma function
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("c733f7"),
Formula(Equal(RisingFactorial(z, k), Div(Gamma(Add(z, k)), Gamma(z)))),
Variables(z, k),
Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)), NotElement(Add(z, k), 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