Fungrim entry: 3c2469

Symbol: FallingFactorial —

\left(z\right)^{\underline{k}}

— Falling factorial

Domain	Codomain
$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$	$\left(z\right)^{\underline{k}} \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \;\implies\; \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`FallingFactorial`	$\left(z\right)^{\underline{k}}$	Falling factorial
`CC`	$\mathbb{C}$	Complex numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("3c2469"),
    SymbolDefinition(FallingFactorial, FallingFactorial(z, k), "Falling factorial"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(z, CC), Element(k, ZZGreaterEqual(0))), Element(FallingFactorial(z, k), CC)))))

Topics using this entry

Factorials and binomial coefficients

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