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Fungrim entry: 19f13b

(z)k=∏i=1k(z+i−1)=∏i=0k−1(z+i)\left(z\right)_{k} = \prod_{i=1}^{k} \left(z + i - 1\right) = \prod_{i=0}^{k - 1} \left(z + i\right)
Assumptions:z∈C  and⁡  k∈Z≥0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
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
Product∏nf(n)\prod_{n} f(n) Product
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("19f13b"),
    Equal(RisingFactorial(z, k), Product(Parentheses(Sub(Add(z, i), 1)), For(i, 1, k)), Product(Parentheses(Add(z, i)), For(i, 0, Sub(k, 1)))),
    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