Fungrim symbol: Binomial

Symbol: Binomial —

{n \choose k}

— Binomial coefficient

Domain	Codomain
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$	${n \choose k} \in \mathbb{Z}_{\ge 0}$
$n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$	${n \choose k} \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`Binomial`	${n \choose k}$	Binomial coefficient
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("def588"),
    SymbolDefinition(Binomial, Binomial(n, k), "Binomial coefficient"),
    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(Binomial(n, k), ZZGreaterEqual(0))), Tuple(And(Element(n, CC), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), CC)))))

Topics using this symbol

The symbol Binomial appears in 17 topics:

Factorials and binomial coefficients (in 28 entries)
Specific values of factorials and binomial coefficients (in 7 entries)
Legendre polynomials (in 7 entries)
Fibonacci numbers (in 6 entries)
Recurrence relations for Bessel functions (in 4 entries)
Chebyshev polynomials (in 4 entries)
Beta function (in 4 entries)
Sine (in 3 entries)
Pi (in 3 entries)
Catalan's constant (in 3 entries)
Bell numbers (in 3 entries)
Stirling numbers (in 1 entries)
Sinc function (in 1 entries)
Gauss hypergeometric function (in 1 entries)
Gamma function (in 1 entries)
Dirichlet L-functions (in 1 entries)
Bernoulli numbers and polynomials (in 1 entries)

Entries using this symbol

The symbol Binomial appears in 76 entries: