# Fungrim entry: bba4ec

$\psi^{(m)}\!\left(z\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1, z\right)$
Assumptions:$m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}$
TeX:
\psi^{(m)}\!\left(z\right) = {\left(-1\right)}^{m + 1} m ! \zeta\!\left(m + 1, z\right)

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Pow${a}^{b}$ Power
Factorial$n !$ Factorial
HurwitzZeta$\zeta\!\left(s, a\right)$ Hurwitz zeta function
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("bba4ec"),
Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(z, CC), NotElement(z, ZZLessEqual(0)))))