Fungrim entry: 56d710

\Gamma\!\left(z + n\right) = \left(z\right)_{n} \Gamma\!\left(z\right)

Assumptions:

z \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}

TeX:

\Gamma\!\left(z + n\right) = \left(z\right)_{n} \Gamma\!\left(z\right)

z \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z}_{\ge 0}

Definitions:

Fungrim symbol	Notation	Short description
`GammaFunction`	$\Gamma\!\left(z\right)$	Gamma function
`RisingFactorial`	$\left(z\right)_{k}$	Rising factorial
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("56d710"),
    Formula(Equal(GammaFunction(Add(z, n)), Mul(RisingFactorial(z, n), GammaFunction(z)))),
    Variables(z, n),
    Assumptions(And(Element(z, SetMinus(CC, ZZLessEqual(0))), Element(n, ZZGreaterEqual(0)))))

Topics using this entry

Gamma function