Fungrim symbol: FallingFactorial

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 symbol

The symbol FallingFactorial appears in 2 topics:

Factorials and binomial coefficients (in 5 entries)
Specific values of factorials and binomial coefficients (in 4 entries)

Entries using this symbol

The symbol FallingFactorial appears in 8 entries: