Fungrim entry: 6e05c9

W_{{k}_{1}}\!\left({z}_{1}\right) \ne W_{{k}_{2}}\!\left({z}_{2}\right)

Assumptions:

{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
`LambertW`	$W\!\left(z\right)$	Lambert W-function
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("6e05c9"),
    Formula(NotEqual(LambertW(Subscript(z, 1), Subscript(k, 1)), LambertW(Subscript(z, 2), Subscript(k, 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(NotEqual(Subscript(k, 1), Subscript(k, 2)), NotEqual(Subscript(z, 1), Subscript(z, 2))), NotElement(LambertW(Subscript(z, 1), Subscript(k, 1)), Set(-1, Neg(Infinity))))))

Topics using this entry

Lambert W-function