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Fungrim entry: 56d4ff

(zk)=(−1)k(k−z−1k){z \choose k} = {\left(-1\right)}^{k} {k - z - 1 \choose k}
Assumptions:z∈C  and⁡  k∈Z≥0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
{z \choose k} = {\left(-1\right)}^{k} {k - z - 1 \choose k}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
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("56d4ff"),
    Formula(Equal(Binomial(z, k), Mul(Pow(-1, k), Binomial(Sub(Sub(k, z), 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.

2021-03-15 19:12:00.328586 UTC