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Fungrim entry: 56d710

Γ ⁣(z+n)=(z)nΓ(z)\Gamma\!\left(z + n\right) = \left(z\right)_{n} \Gamma(z)
Assumptions:zC{0,1,}  and  nZ0z \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
\Gamma\!\left(z + n\right) = \left(z\right)_{n} \Gamma(z)

z \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
GammaΓ(z)\Gamma(z) Gamma function
RisingFactorial(z)k\left(z\right)_{k} Rising factorial
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(Gamma(Add(z, n)), Mul(RisingFactorial(z, n), Gamma(z)))),
    Variables(z, n),
    Assumptions(And(Element(z, SetMinus(CC, ZZLessEqual(0))), Element(n, ZZGreaterEqual(0)))))

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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