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Fungrim entry: 6c6d3e

logG ⁣(z)={logG(z),z(,0]logG(z),otherwise\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:zCz \in \mathbb{C}
\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}
Fungrim symbol Notation Short description
LogBarnesGlogG(z)\log G(z) Logarithmic Barnes G-function
Conjugatez\overline{z} Complex conjugate
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(LogBarnesG(Conjugate(z)), Cases(Tuple(LogBarnesG(z), Element(z, OpenClosedInterval(Neg(Infinity), 0))), Tuple(Conjugate(LogBarnesG(z)), Otherwise)))),
    Assumptions(Element(z, CC)))

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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