Fungrim entry: e5bba3

\operatorname{Im}\!\left(W_{-1}\!\left(z\right)\right) \in \left(-3 \pi, 0\right]

Assumptions:

z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

\operatorname{Im}\!\left(W_{-1}\!\left(z\right)\right) \in \left(-3 \pi, 0\right]

z \in \mathbb{C} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Im`	$\operatorname{Im}(z)$	Imaginary part
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("e5bba3"),
    Formula(Element(Im(LambertW(z, -1)), OpenClosedInterval(Neg(Mul(3, Pi)), 0))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

Lambert W-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