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Fungrim entry: d7136f

solutionswC[wew=z]={Wk ⁣(z):kZand(z0ork=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}
TeX:
\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}
Definitions:
Fungrim symbol Notation Short description
SolutionssolutionsP(x)Q ⁣(x)\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right) Solution set
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("d7136f"),
    Formula(Equal(Solutions(Brackets(Equal(Mul(w, Exp(w)), z)), w, Element(w, CC)), SetBuilder(LambertW(k, z), k, And(Element(k, ZZ), Or(Unequal(z, 0), Equal(k, 0)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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2019-09-16 21:17:18.797188 UTC