Fungrim home page

Fungrim entry: 4228cd

Bn ⁣(z)=−nζ ⁣(1−n,z)B_{n}\!\left(z\right) = -n \zeta\!\left(1 - n, z\right)
Assumptions:n∈Z≥1  and⁡  z∈Cn \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
B_{n}\!\left(z\right) = -n \zeta\!\left(1 - n, z\right)

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
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("4228cd"),
    Formula(Equal(BernoulliPolynomial(n, z), Neg(Mul(n, HurwitzZeta(Sub(1, n), z))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(z, 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