# Fungrim entry: af31ae

$\frac{d}{d z}\, \left[\log G(z)\right] = \left(z - 1\right) \psi\!\left(z\right) - z + \frac{\log\!\left(2 \pi\right) + 1}{2}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}$
TeX:
\frac{d}{d z}\, \left[\log G(z)\right] = \left(z - 1\right) \psi\!\left(z\right) - z + \frac{\log\!\left(2 \pi\right) + 1}{2}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
ComplexBranchDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative, allowing branch cuts
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
DigammaFunction$\psi\!\left(z\right)$ Digamma function
Log$\log(z)$ Natural logarithm
Pi$\pi$ The constant pi (3.14...)
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("af31ae"),
Variables(z),
Assumptions(And(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