Fungrim entry: d9a7a3

\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:

z \in \mathbb{C}

TeX:

\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}

Definitions:

Fungrim symbol	Notation	Short description
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`Abs`	$\left\|z\right\|$	Absolute value
`LogBarnesG`	$\log G(z)$	Logarithmic Barnes G-function
`Log`	$\log(z)$	Natural logarithm
`BarnesG`	$G(z)$	Barnes G-function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("d9a7a3"),
    Formula(Implies(Or(Element(z, OpenInterval(0, Infinity)), Less(Abs(Sub(z, Decimal("2.5"))), Decimal("2.5"))), Equal(LogBarnesG(z), Log(BarnesG(z))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Barnes G-function