Fungrim entry: 84196a

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

Assumptions:

n \in \mathbb{Z}_{\ge 2} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C}

TeX:

\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}

Definitions:

Fungrim symbol	Notation	Short description
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function
`Pow`	${a}^{b}$	Power
`Factorial`	$n !$	Factorial
`DigammaFunction`	$\psi\!\left(z\right)$	Digamma function
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("84196a"),
    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))))

Topics using this entry

Hurwitz zeta function