Fungrim entry: 88168b

W_{k}\!\left(z\right) \exp\!\left(W_{k}\!\left(z\right)\right) = z

Assumptions:

\left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}\right) \;\mathbin{\operatorname{or}}\; \left(k = 0 \;\mathbin{\operatorname{and}}\; z = 0\right)

TeX:

W_{k}\!\left(z\right) \exp\!\left(W_{k}\!\left(z\right)\right) = z

\left(k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}\right) \;\mathbin{\operatorname{or}}\; \left(k = 0 \;\mathbin{\operatorname{and}}\; z = 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`Exp`	${e}^{z}$	Exponential function
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("88168b"),
    Formula(Equal(Mul(LambertW(z, k), Exp(LambertW(z, k))), z)),
    Variables(k, z),
    Assumptions(Or(And(Element(k, ZZ), Element(z, SetMinus(CC, Set(0)))), And(Equal(k, 0), Equal(z, 0)))))

Topics using this entry

Lambert W-function