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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[z] > Transformations > Products, sums, and powers of the direct function > Sums of the direct function





http://functions.wolfram.com/01.31.16.0004.01









  


  








Input Form





ProductLog[x] + ProductLog[y] == ProductLog[x y (1/ProductLog[x] + 1/ProductLog[y])] /; x > 0 || y > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["ProductLog", "[", "x", "]"]], "+", RowBox[List["ProductLog", "[", "y", "]"]]]], "\[Equal]", RowBox[List["ProductLog", "[", RowBox[List["x", " ", "y", " ", RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["ProductLog", "[", "x", "]"]]], "+", FractionBox["1", RowBox[List["ProductLog", "[", "y", "]"]]]]], ")"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["x", ">", "0"]], "\[Or]", RowBox[List["y", ">", "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> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mi> y </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> W </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mi> y </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <ci> W </ci> <ci> x </ci> </apply> <apply> <ci> W </ci> <ci> y </ci> </apply> </apply> <apply> <ci> W </ci> <apply> <times /> <ci> x </ci> <ci> y </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> W </ci> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> W </ci> <ci> y </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> y </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ProductLog", "[", "x_", "]"]], "+", RowBox[List["ProductLog", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductLog", "[", RowBox[List["x", " ", "y", " ", RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["ProductLog", "[", "x", "]"]]], "+", FractionBox["1", RowBox[List["ProductLog", "[", "y", "]"]]]]], ")"]]]], "]"]], "/;", RowBox[List[RowBox[List["x", ">", "0"]], "||", RowBox[List["y", ">", "0"]]]]]]]]]]


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





2001-10-29