# Fungrim entry: 6db9fc

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

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
DigammaFunction$\psi\!\left(z\right)$ Digamma 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("6db9fc"),
Formula(Equal(ComplexDerivative(Brackets(DigammaFunction(z)), For(z, z, n)), DigammaFunction(z, n))),
Variables(n, z),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(z, CC), NotElement(z, ZZLessEqual(0)))))

## 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