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Fungrim entry: 88168b

Wk ⁣(z)exp ⁣(Wk ⁣(z))=zW_{k}\!\left(z\right) \exp\!\left(W_{k}\!\left(z\right)\right) = z
Assumptions:(kZ  and  zC{0})  or  (k=0  and  z=0)\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
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
Expez{e}^{z} Exponential function
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("88168b"),
    Formula(Equal(Mul(LambertW(k, z), Exp(LambertW(k, z))), z)),
    Variables(k, z),
    Assumptions(Or(And(Element(k, ZZ), Element(z, SetMinus(CC, Set(0)))), And(Equal(k, 0), Equal(z, 0)))))

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2020-04-08 16:14:44.404316 UTC