# Fungrim entry: 5a11eb

$\log G(x) = \begin{cases} \log\!\left(G(x)\right), & x > 0\\\log\!\left(\left|G(x)\right|\right) + \frac{1}{2} n \left(n - 1\right) \pi i, & \text{otherwise}\\ \end{cases}\; \text{ where } n = \left\lfloor x \right\rfloor$
Assumptions:$x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x \notin \{0, -1, \ldots\}$
TeX:
\log G(x) = \begin{cases} \log\!\left(G(x)\right), & x > 0\\\log\!\left(\left|G(x)\right|\right) + \frac{1}{2} n \left(n - 1\right) \pi i, & \text{otherwise}\\ \end{cases}\; \text{ where } n = \left\lfloor x \right\rfloor

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
Log$\log(z)$ Natural logarithm
BarnesG$G(z)$ Barnes G-function
Abs$\left|z\right|$ Absolute value
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
RR$\mathbb{R}$ Real numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("5a11eb"),
Formula(Equal(LogBarnesG(x), Where(Cases(Tuple(Log(BarnesG(x)), Greater(x, 0)), Tuple(Add(Log(Abs(BarnesG(x))), Mul(Mul(Mul(Mul(Div(1, 2), n), Sub(n, 1)), Pi), ConstI)), Otherwise)), Equal(n, Floor(x))))),
Variables(x),
Assumptions(And(Element(x, RR), NotElement(x, 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