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Fungrim entry: c640bf

(−z)k=(−1)k(z−k+1)k\left(-z\right)_{k} = {\left(-1\right)}^{k} \left(z - k + 1\right)_{k}
Assumptions:z∈C and⁡ k∈Z≥0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}
TeX:
\left(-z\right)_{k} = {\left(-1\right)}^{k} \left(z - k + 1\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
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("c640bf"),
    Formula(Equal(RisingFactorial(Neg(z), k), Mul(Pow(-1, k), RisingFactorial(Add(Sub(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.

2019-06-18 07:49:59.356594 UTC