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Fungrim entry: fe9fb7

(z)k+1=(z+k)(z)k\left(z\right)_{k + 1} = \left(z + k\right) \left(z\right)_{k}
Assumptions:zCandkZ0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
\left(z\right)_{k + 1} = \left(z + k\right) \left(z\right)_{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
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("fe9fb7"),
    Formula(Equal(RisingFactorial(z, Add(k, 1)), Mul(Add(z, k), RisingFactorial(z, 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