# Fungrim entry: 2d3356

$\left\{ W_{0}\!\left(z\right) : z \in \mathbb{C} \setminus \mathbb{R} \right\} = \left\{ x + y i : y \in \left(-\pi, \pi\right) \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, x \in \left(-y \cot(y), \infty\right) \right\}$
TeX:
\left\{ W_{0}\!\left(z\right) : z \in \mathbb{C} \setminus \mathbb{R} \right\} = \left\{ x + y i : y \in \left(-\pi, \pi\right) \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, x \in \left(-y \cot(y), \infty\right) \right\}
Definitions:
Fungrim symbol Notation Short description
LambertW$W_{k}\!\left(z\right)$ Lambert W-function
CC$\mathbb{C}$ Complex numbers
RR$\mathbb{R}$ Real numbers
ConstI$i$ Imaginary unit
OpenInterval$\left(a, b\right)$ Open interval
Pi$\pi$ The constant pi (3.14...)
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("2d3356"),
Formula(Equal(Set(LambertW(0, z), ForElement(z, SetMinus(CC, RR))), Set(Add(x, Mul(y, ConstI)), For(Tuple(x, y)), And(Element(y, SetMinus(OpenInterval(Neg(Pi), Pi), Set(0))), Element(x, OpenInterval(Mul(Neg(y), Cot(y)), Infinity)))))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC