Fungrim entry: 5bdba2

\zeta\!\left(-n, a\right) = -\frac{B_{n + 1}\!\left(a\right)}{n + 1}

Assumptions:

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}

TeX:

\zeta\!\left(-n, a\right) = -\frac{B_{n + 1}\!\left(a\right)}{n + 1}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`BernoulliPolynomial`	$B_{n}\!\left(z\right)$	Bernoulli polynomial
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("5bdba2"),
    Formula(Equal(HurwitzZeta(Neg(n), a), Neg(Div(BernoulliPolynomial(Add(n, 1), a), Add(n, 1))))),
    Variables(n, a),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(a, CC))))

Topics using this entry

Hurwitz zeta function

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