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\!\left(y\right), \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\!\left(y\right), \infty\right) \right\}

Definitions:

Fungrim symbol	Notation	Short description
`SetBuilder`	$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$	Set comprehension
`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
`ConstPi`	$\pi$	The constant pi (3.14...)
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("2d3356"),
    Formula(Equal(SetBuilder(LambertW(0, z), z, Element(z, SetMinus(CC, RR))), SetBuilder(Add(x, Mul(y, ConstI)), Tuple(x, y), And(Element(y, SetMinus(OpenInterval(Neg(ConstPi), ConstPi), Set(0))), Element(x, OpenInterval(Mul(Neg(y), Cot(y)), Infinity)))))))

Topics using this entry

Lambert W-function