w^w == z /; w == Log[z]/ProductLog[Log[z]]

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["w", "w"], "\[Equal]", "z"]], "/;", RowBox[List["w", "\[Equal]", FractionBox[RowBox[List[RowBox[List["Log", "[", "z", "]"]], " "]], RowBox[List["ProductLog", "[", RowBox[List["Log", "[", "z", "]"]], "]"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> w </mi> <mi> w </mi> </msup> <mo> &#10869; </mo> <mi> z </mi> </mrow> <mo> /; </mo> <mrow> <mi> w </mi> <mo> &#10869; </mo> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <ci> w </ci> <ci> w </ci> </apply> <ci> z </ci> </apply> <apply> <eq /> <ci> w </ci> <apply> <times /> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> W </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["w_", "w_"], "]"]], "\[RuleDelayed]", RowBox[List["z", "/;", RowBox[List["w", "\[Equal]", FractionBox[RowBox[List["Log", "[", "z", "]"]], RowBox[List["ProductLog", "[", RowBox[List["Log", "[", "z", "]"]], "]"]]]]]]]]]]]

2001-10-29