Fungrim symbol: BernoulliPolynomial

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 symbol

The symbol BernoulliPolynomial appears in 7 topics:

Bernoulli numbers and polynomials (in 17 entries)
Hurwitz zeta function (in 3 entries)
Barnes G-function (in 2 entries)
Riemann zeta function (in 1 entries)
General analytic functions (in 1 entries)
Gamma function (in 1 entries)
Dirichlet L-functions (in 1 entries)

Entries using this symbol

The symbol BernoulliPolynomial appears in 25 entries: