Fungrim entry: 44ad09

\left\{ W\!\left(x\right) : x \in \left(-\infty, -{e}^{-1}\right) \right\} = \left\{ -y \cot(y) + y i : y \in \left(0, \pi\right) \right\}

TeX:

\left\{ W\!\left(x\right) : x \in \left(-\infty, -{e}^{-1}\right) \right\} = \left\{ -y \cot(y) + y i : y \in \left(0, \pi\right) \right\}

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("44ad09"),
    Formula(Equal(Set(LambertW(x), ForElement(x, OpenInterval(Neg(Infinity), Neg(Exp(-1))))), Set(Add(Mul(Neg(y), Cot(y)), Mul(y, ConstI)), ForElement(y, OpenInterval(0, Pi))))))

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