Fungrim entry: a044e1

\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}

TeX:

\operatorname{Im}\!\left(\log G(x)\right) = \frac{n \left(n - 1\right)}{2} \pi\; \text{ where } n = \left\lfloor x \right\rfloor

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x < 0 \;\mathbin{\operatorname{and}}\; x \notin \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Im`	$\operatorname{Im}(z)$	Imaginary part
`LogBarnesG`	$\log G(z)$	Logarithmic Barnes G-function
`Pi`	$\pi$	The constant pi (3.14...)
`RR`	$\mathbb{R}$	Real numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("a044e1"),
    Formula(Equal(Im(LogBarnesG(x)), Where(Mul(Div(Mul(n, Sub(n, 1)), 2), Pi), Equal(n, Floor(x))))),
    Variables(x),
    Assumptions(And(Element(x, RR), Less(x, 0), NotElement(x, ZZ))))

Topics using this entry

Barnes G-function