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Fungrim entry: 1d5e92

(zk)=(z)k‾k!{z \choose k} = \frac{\left(z\right)^{\underline{k}}}{k !}
Assumptions:z∈C  and⁡  k∈Z≥0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
TeX:
{z \choose k} = \frac{\left(z\right)^{\underline{k}}}{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
FallingFactorial(z)k‾\left(z\right)^{\underline{k}} Falling factorial
Factorialn!n ! Factorial
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("1d5e92"),
    Formula(Equal(Binomial(z, k), Div(FallingFactorial(z, k), Factorial(k)))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)))))

Topics using this entry

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