Fungrim symbol: StirlingS1

Symbol: StirlingS1 —

s\!\left(n, k\right)

— Signed Stirling number of the first kind

Domain	Codomain
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$	$s\!\left(n, k\right) \in \mathbb{Z}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`StirlingS1`	$s\!\left(n, k\right)$	Signed Stirling number of the first kind
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("2e9d0c"),
    SymbolDefinition(StirlingS1, StirlingS1(n, k), "Signed Stirling number of the first kind"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0))), Element(StirlingS1(n, k), ZZ)))))

Topics using this symbol

The symbol StirlingS1 appears in 2 topics:

Stirling numbers (in 5 entries)
Factorials and binomial coefficients (in 1 entries)

Entries using this symbol

The symbol StirlingS1 appears in 6 entries: