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Fungrim entry: e78989

(z)k=(z+k1)k\left(z\right)_{k} = \left(z + k - 1\right)^{\underline{k}}
Assumptions:zCandkZ0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
\left(z\right)_{k} = \left(z + k - 1\right)^{\underline{k}}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
RisingFactorial(z)k\left(z\right)_{k} Rising factorial
FallingFactorial(z)k\left(z\right)^{\underline{k}} Falling factorial
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("e78989"),
    Formula(Equal(RisingFactorial(z, k), FallingFactorial(Sub(Add(z, k), 1), k))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, 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.

2019-08-21 11:44:15.926409 UTC