# 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC