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Fungrim entry: f80439

Bn ⁣(−x)=(−1)n(Bn ⁣(x)+nxn−1)B_{n}\!\left(-x\right) = {\left(-1\right)}^{n} \left(B_{n}\!\left(x\right) + n {x}^{n - 1}\right)
Assumptions:n∈Z≥0  and⁡  x∈Cn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
B_{n}\!\left(-x\right) = {\left(-1\right)}^{n} \left(B_{n}\!\left(x\right) + n {x}^{n - 1}\right)

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Powab{a}^{b} Power
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("f80439"),
    Formula(Equal(BernoulliPolynomial(n, Neg(x)), Mul(Pow(-1, n), Add(BernoulliPolynomial(n, x), Mul(n, Pow(x, Sub(n, 1))))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC