Fungrim symbol: Factorial

Symbol: Factorial —

n !

— Factorial

Domain	Codomain
$n \in \mathbb{Z}_{\ge 0}$	$n ! \in \mathbb{Z}_{\ge 1}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`Factorial`	$n !$	Factorial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("81aeba"),
    SymbolDefinition(Factorial, Factorial(n), "Factorial"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(Element(n, ZZGreaterEqual(0)), Element(Factorial(n), ZZGreaterEqual(1))))))

Topics using this symbol

The symbol Factorial appears in 38 topics:

Factorials and binomial coefficients (in 20 entries)
Digamma function (in 15 entries)
Confluent hypergeometric functions (in 9 entries)
Bell numbers (in 7 entries)
Pi (in 6 entries)
Stirling numbers (in 5 entries)
Specific values of factorials and binomial coefficients (in 5 entries)
Riemann zeta function (in 5 entries)
General analytic functions (in 5 entries)
Gauss hypergeometric function (in 5 entries)
Chebyshev polynomials (in 5 entries)
Bernoulli numbers and polynomials (in 5 entries)
Specific values of the digamma function (in 4 entries)
Recurrence relations for Bessel functions (in 4 entries)
Hurwitz zeta function (in 4 entries)
Sinc function (in 3 entries)
Series representations of Carlson symmetric elliptic integrals (in 3 entries)
Lambert W-function (in 3 entries)
Exponential function (in 3 entries)
Barnes G-function (in 3 entries)
Stieltjes constants (in 2 entries)
Square roots (in 2 entries)
Sine (in 2 entries)
Series and product representations of Jacobi theta functions (in 2 entries)
Inverse tangent (in 2 entries)
Gamma function (in 2 entries)
Symbolic expressions (in 1 entries)
Multiple zeta values (in 1 entries)
Legendre polynomials (in 1 entries)
Keiper-Li coefficients (in 1 entries)
Integer sequences (in 1 entries)
Fibonacci numbers (in 1 entries)
Euler's constant (in 1 entries)
Dirichlet L-functions (in 1 entries)
Coulomb wave functions (in 1 entries)
Bounds and inequalities for the gamma function (in 1 entries)
Beta function (in 1 entries)
Arithmetic-geometric mean (in 1 entries)

Entries using this symbol

The symbol Factorial appears in 133 entries: