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Fungrim entry: d9a7a3

(z(0,)  or  z2.5<2.5)        (logG(z)=log ⁣(G(z)))\left(z \in \left(0, \infty\right) \;\mathbin{\operatorname{or}}\; \left|z - 2.5\right| < 2.5\right) \;\implies\; \left(\log G(z) = \log\!\left(G(z)\right)\right)
Assumptions:zCz \in \mathbb{C}
\left(z \in \left(0, \infty\right) \;\mathbin{\operatorname{or}}\; \left|z - 2.5\right| < 2.5\right) \;\implies\; \left(\log G(z) = \log\!\left(G(z)\right)\right)

z \in \mathbb{C}
Fungrim symbol Notation Short description
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Absz\left|z\right| Absolute value
LogBarnesGlogG(z)\log G(z) Logarithmic Barnes G-function
Loglog(z)\log(z) Natural logarithm
BarnesGG(z)G(z) Barnes G-function
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Implies(Or(Element(z, OpenInterval(0, Infinity)), Less(Abs(Sub(z, Decimal("2.5"))), Decimal("2.5"))), Equal(LogBarnesG(z), Log(BarnesG(z))))),
    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