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Fungrim entry: d7136f

solutionswC[wew=z]={Wk ⁣(z):kZ  and  (z0  or  k=0)}\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[w {e}^{w} = z\right] = \left\{ W_{k}\!\left(z\right) : k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(z \ne 0 \;\mathbin{\operatorname{or}}\; k = 0\right) \right\}
Assumptions:zCz \in \mathbb{C}
\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[w {e}^{w} = z\right] = \left\{ W_{k}\!\left(z\right) : k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(z \ne 0 \;\mathbin{\operatorname{or}}\; k = 0\right) \right\}

z \in \mathbb{C}
Fungrim symbol Notation Short description
SolutionssolutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x) Solution set
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
LambertWW ⁣(z)W\!\left(z\right) Lambert W-function
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Equal(Solutions(Brackets(Equal(Mul(w, Exp(w)), z)), ForElement(w, CC)), Set(LambertW(z, k), For(k), And(Element(k, ZZ), Or(NotEqual(z, 0), Equal(k, 0)))))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC