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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.32.27.0005.01









  


  








Input Form





Log[ProductLog[-1, x]] == Log[x] - ProductLog[-1, x] /; -(1/E) < x < 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", "x"]], "]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "x", "]"]], "-", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", "x"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["1", "\[ExponentialE]"]]], "<", "x", "<", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> W </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> W </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> &#8519; </mi> </mfrac> </mrow> <mo> &lt; </mo> <mi> x </mi> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ln /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <cn type='integer'> -1 </cn> </apply> <ci> x </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <cn type='integer'> -1 </cn> </apply> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", "x_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "x", "]"]], "-", RowBox[List["ProductLog", "[", RowBox[List[RowBox[List["-", "1"]], ",", "x"]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["1", "\[ExponentialE]"]]], "<", "x", "<", "0"]]]]]]]]


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





2001-10-29