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Fungrim entry: 84196a

ζ ⁣(n,a)=(1)n(n1)!ψ(n1) ⁣(a)\zeta\!\left(n, a\right) = \frac{{\left(-1\right)}^{n}}{\left(n - 1\right)!} \psi^{(n - 1)}\!\left(a\right)
Assumptions:nZ2  and  aCn \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}
\zeta\!\left(n, a\right) = \frac{{\left(-1\right)}^{n}}{\left(n - 1\right)!} \psi^{(n - 1)}\!\left(a\right)

n \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}
Fungrim symbol Notation Short description
HurwitzZetaζ ⁣(s,a)\zeta\!\left(s, a\right) Hurwitz zeta function
Powab{a}^{b} Power
Factorialn!n ! Factorial
DigammaFunctionψ ⁣(z)\psi\!\left(z\right) Digamma function
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(n, a), Mul(Div(Pow(-1, n), Factorial(Sub(n, 1))), DigammaFunction(a, Sub(n, 1))))),
    Variables(n, a),
    Assumptions(And(Element(n, ZZGreaterEqual(2)), Element(a, CC))))

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2021-03-15 19:12:00.328586 UTC