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Fungrim entry: 1f88a4

Symbol: BernoulliPolynomial Bn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Domain Codomain
nZ0andzRn \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} Bn ⁣(z)RB_{n}\!\left(z\right) \in \mathbb{R}
nZ0andzCn \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} Bn ⁣(z)CB_{n}\!\left(z\right) \in \mathbb{C}
nZ0andzRandRRingsandQRn \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 Bn ⁣(z)RB_{n}\!\left(z\right) \in R
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
RRR\mathbb{R} Real numbers
CCC\mathbb{C} Complex numbers
QQQ\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)))))

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

2019-11-19 15:10:20.037976 UTC