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Fungrim entry: c733f7

(z)k=Γ ⁣(z+k)Γ(z)\left(z\right)_{k} = \frac{\Gamma\!\left(z + k\right)}{\Gamma(z)}
Assumptions:zC  and  kZ0  and  z+k{0,1,}z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z + k \notin \{0, -1, \ldots\}
\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\}
Fungrim symbol Notation Short description
RisingFactorial(z)k\left(z\right)_{k} Rising factorial
GammaΓ(z)\Gamma(z) Gamma function
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    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)))))

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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