Fungrim entry: 1f88a4

Symbol: BernoulliPolynomial —

B_{n}\!\left(z\right)

— Bernoulli polynomial

Domain	Codomain
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{R}$	$B_{n}\!\left(z\right) \in \mathbb{R}$
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}$	$B_{n}\!\left(z\right) \in \mathbb{C}$
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in R \;\mathbin{\operatorname{and}}\; R \in \operatorname{Rings} \;\mathbin{\operatorname{and}}\; \mathbb{Q} \subseteq R$	$B_{n}\!\left(z\right) \in R$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`BernoulliPolynomial`	$B_{n}\!\left(z\right)$	Bernoulli polynomial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`RR`	$\mathbb{R}$	Real numbers
`CC`	$\mathbb{C}$	Complex numbers
`QQ`	$\mathbb{Q}$	Rational numbers

Source code for this entry:

Entry(ID("1f88a4"),
    SymbolDefinition(BernoulliPolynomial, BernoulliPolynomial(n, z), "Bernoulli polynomial"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(z, RR)), Element(BernoulliPolynomial(n, z), RR)), Tuple(And(Element(n, ZZGreaterEqual(0)), Element(z, CC)), Element(BernoulliPolynomial(n, z), CC)), Tuple(And(Element(n, ZZGreaterEqual(0)), Element(z, R), Element(R, Rings), SubsetEqual(QQ, R)), Element(BernoulliPolynomial(n, z), R)))))

Topics using this entry

Bernoulli numbers and polynomials