Fungrim symbol: RisingFactorial

Symbol: RisingFactorial —

\left(z\right)_{k}

— Rising factorial

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

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`RisingFactorial`	$\left(z\right)_{k}$	Rising 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("579595"),
    SymbolDefinition(RisingFactorial, RisingFactorial(z, k), "Rising 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(RisingFactorial(z, k), CC)))))

Topics using this symbol

The symbol RisingFactorial appears in 12 topics:

Factorials and binomial coefficients (in 12 entries)
Confluent hypergeometric functions (in 8 entries)
Series representations of Carlson symmetric elliptic integrals (in 6 entries)
Specific values of factorials and binomial coefficients (in 4 entries)
Gauss hypergeometric function (in 4 entries)
Chebyshev polynomials (in 4 entries)
Stirling numbers (in 3 entries)
Square roots (in 3 entries)
Riemann zeta function (in 2 entries)
Hurwitz zeta function (in 2 entries)
Gamma function (in 2 entries)
Digamma function (in 2 entries)

Entries using this symbol

The symbol RisingFactorial appears in 50 entries: