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Fungrim entry: 6e05c9

Wk1 ⁣(z1)Wk2 ⁣(z2)W_{{k}_{1}}\!\left({z}_{1}\right) \ne W_{{k}_{2}}\!\left({z}_{2}\right)
Assumptions:k1Zandk2Zandz1Candz2Cand(k1k2orz1z2)andWk1 ⁣(z1){1,}{k}_{1} \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, {k}_{2} \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, {z}_{1} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {z}_{2} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left({k}_{1} \ne {k}_{2} \,\mathbin{\operatorname{or}}\, {z}_{1} \ne {z}_{2}\right) \,\mathbin{\operatorname{and}}\, W_{{k}_{1}}\!\left({z}_{1}\right) \notin \left\{-1, -\infty\right\}
TeX:
W_{{k}_{1}}\!\left({z}_{1}\right) \ne W_{{k}_{2}}\!\left({z}_{2}\right)

{k}_{1} \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, {k}_{2} \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, {z}_{1} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, {z}_{2} \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left({k}_{1} \ne {k}_{2} \,\mathbin{\operatorname{or}}\, {z}_{1} \ne {z}_{2}\right) \,\mathbin{\operatorname{and}}\, W_{{k}_{1}}\!\left({z}_{1}\right) \notin \left\{-1, -\infty\right\}
Definitions:
Fungrim symbol Notation Short description
LambertWWk ⁣(z)W_{k}\!\left(z\right) Lambert W-function
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("6e05c9"),
    Formula(Unequal(LambertW(Subscript(k, 1), Subscript(z, 1)), LambertW(Subscript(k, 2), Subscript(z, 2)))),
    Variables(Subscript(k, 1), Subscript(z, 1), Subscript(k, 2), Subscript(z, 2)),
    Assumptions(And(Element(Subscript(k, 1), ZZ), Element(Subscript(k, 2), ZZ), Element(Subscript(z, 1), CC), Element(Subscript(z, 2), CC), Or(Unequal(Subscript(k, 1), Subscript(k, 2)), Unequal(Subscript(z, 1), Subscript(z, 2))), NotElement(LambertW(Subscript(k, 1), Subscript(z, 1)), Set(-1, Neg(Infinity))))))

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2019-10-05 13:11:19.856591 UTC