# 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

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