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Fungrim entry: 5bdba2

ζ ⁣(n,a)=Bn+1 ⁣(a)n+1\zeta\!\left(-n, a\right) = -\frac{B_{n + 1}\!\left(a\right)}{n + 1}
Assumptions:nZ0  and  aCn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}
\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}
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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))))

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2021-03-15 19:12:00.328586 UTC