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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/01.31.27.0002.01









  


  








Input Form





E^(\[Alpha] ProductLog[z]) == z^\[Alpha]/ProductLog[z]^\[Alpha]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[Alpha]", " ", RowBox[List["ProductLog", "[", "z", "]"]]]]], "\[Equal]", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", SuperscriptBox[RowBox[List["ProductLog", "[", "z", "]"]], RowBox[List["-", "\[Alpha]"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#10869; </mo> <mrow> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> <mo> &#8290; </mo> <msup> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> &#945; </ci> <apply> <ci> W </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> &#945; </ci> </apply> <apply> <power /> <apply> <ci> W </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["\[Alpha]_", " ", RowBox[List["ProductLog", "[", "z_", "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", SuperscriptBox[RowBox[List["ProductLog", "[", "z", "]"]], RowBox[List["-", "\[Alpha]"]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29