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Fungrim entry: 41f950

(z+1)k=z+kz(z)k\left(z + 1\right)_{k} = \frac{z + k}{z} \left(z\right)_{k}
Assumptions:zC{0}  and  kZ0z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
\left(z + 1\right)_{k} = \frac{z + k}{z} \left(z\right)_{k}

z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
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:
    Formula(Equal(RisingFactorial(Add(z, 1), k), Mul(Div(Add(z, k), z), RisingFactorial(z, k)))),
    Variables(z, k),
    Assumptions(And(Element(z, SetMinus(CC, Set(0))), 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.

2021-03-15 19:12:00.328586 UTC