Fungrim entry: 82926c

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

Assumptions:

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

TeX:

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

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

Definitions:

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

Source code for this entry:

Entry(ID("82926c"),
    Formula(Element(Im(LambertW(1, z)), OpenInterval(0, Mul(3, ConstPi)))),
    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.

2019-06-18 07:49:59.356594 UTC