Fungrim home page

Fungrim entry: c2dcfa

Bn ⁣(1−x)=(−1)nBn ⁣(x)B_{n}\!\left(1 - x\right) = {\left(-1\right)}^{n} B_{n}\!\left(x\right)
Assumptions:n∈Z≥0  and⁡  x∈Cn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
B_{n}\!\left(1 - x\right) = {\left(-1\right)}^{n} B_{n}\!\left(x\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("c2dcfa"),
    Formula(Equal(BernoulliPolynomial(n, Sub(1, x)), Mul(Pow(-1, n), BernoulliPolynomial(n, x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(x, CC))))

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