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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/01.32.27.0003.01









  


  








Input Form





Log[ProductLog[k, z]] == Log[z] - ProductLog[k, z] + 2 I Pi k








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "k"]]]]]]]]








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> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> W </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> W </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo fontweight='normal' fontstyle='normal'> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ln /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> k </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> k </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["ProductLog", "[", RowBox[List["k_", ",", "z_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "k"]]]]]]]]


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





2001-10-29