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

Barnes G-function

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