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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[z] > Series representations > Generalized power series > Expansions at z==-1/e





http://functions.wolfram.com/01.31.06.0006.02









  


  








Input Form





ProductLog[z] \[Proportional] -1 + O[Sqrt[z + 1/E]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ProductLog", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["O", "[", SqrtBox[RowBox[List["z", "+", FractionBox["1", "\[ExponentialE]"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mi> &#8519; </mi> </mfrac> </mrow> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> W </ci> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <ci> O </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ProductLog", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["O", "[", RowBox[List["z", "+", FractionBox["1", "\[ExponentialE]"]]], "]"]]]]]]]]]


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





2001-10-29