Fungrim entry: 6c6d3e

$\log G\!\left(\overline{z}\right) = \begin{cases} \log G(z), & z \in \left(-\infty, 0\right]\\\overline{\log G(z)}, & \text{otherwise}\\ \end{cases}$
Assumptions:$z \in \mathbb{C}$
TeX:
\log G\!\left(\overline{z}\right) = \begin{cases} \log G(z), & z \in \left(-\infty, 0\right]\\\overline{\log G(z)}, & \text{otherwise}\\ \end{cases}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
LogBarnesG$\log G(z)$ Logarithmic Barnes G-function
Conjugate$\overline{z}$ Complex conjugate
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("6c6d3e"),
Formula(Equal(LogBarnesG(Conjugate(z)), Cases(Tuple(LogBarnesG(z), Element(z, OpenClosedInterval(Neg(Infinity), 0))), Tuple(Conjugate(LogBarnesG(z)), Otherwise)))),
Variables(z),
Assumptions(Element(z, CC)))

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