Fungrim home page

Fungrim entry: c733f7

(z)k=Γ ⁣(z+k)Γ(z)\left(z\right)_{k} = \frac{\Gamma\!\left(z + k\right)}{\Gamma(z)}
Assumptions:zCandkZ0andz+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\}
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(z)k\left(z\right)_{k} Rising factorial
GammaFunctionΓ(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:
Entry(ID("c733f7"),
    Formula(Equal(RisingFactorial(z, k), Div(GammaFunction(Add(z, k)), GammaFunction(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.

2019-10-05 13:11:19.856591 UTC