z == w E^w /; w == ProductLog[k, z] && Element[k, Integers]

Cell[BoxData[RowBox[List[RowBox[List["z", "\[Equal]", RowBox[List["w", " ", SuperscriptBox["\[ExponentialE]", "w"]]]]], "/;", " ", RowBox[List[RowBox[List["w", "\[Equal]", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> z </mi> <mo> &#10869; </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mi> w </mi> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#10869; </mo> <mrow> <msub> <mi> W </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <ci> z </ci> <apply> <times /> <ci> w </ci> <apply> <power /> <exponentiale /> <ci> w </ci> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <ci> w </ci> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> k </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "z_", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["w", " ", SuperscriptBox["\[ExponentialE]", "w"]]], "/;", RowBox[List[RowBox[List["w", "\[Equal]", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]]]

2001-10-29