# Fungrim entry: a044e1

$\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor$
Assumptions:$x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}$
TeX:
\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Im$\operatorname{Im}(z)$ Imaginary part
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
Pi$\pi$ The constant pi (3.14...)
RR$\mathbb{R}$ Real numbers
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("a044e1"),
Formula(Equal(Im(LogBarnesG(x)), Where(Mul(Div(Mul(n, Sub(n, 1)), 2), Pi), Equal(n, Floor(x))))),
Variables(x),
Assumptions(And(Element(x, RR), Less(x, 0), NotElement(x, ZZ))))

## 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