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variants of this functions
ProductLog




Mathematica Notation

Traditional Notation









Elementary Functions > ProductLog[k,z] > General characteristics > Domain and analyticity





http://functions.wolfram.com/01.32.04.0001.01









  


  








Input Form





DomainAndRange[Function[{k, z}, ProductLog[k, z]]] == ProductSet[Integers, Complexes] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["k", ",", " ", "z"]], "}"]], ",", RowBox[List["ProductLog", "[", RowBox[List["k", ",", "z"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]








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> <mo> ( </mo> <mrow> <mi> k </mi> <mo> &#8902; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <msub> <mi> W </mi> <mi> k </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> k </ci> <ci> z </ci> </apply> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> k </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <integers /> <ci> &#8450; </ci> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["k_", ",", "z_"]], "}"]], ",", RowBox[List["ProductLog", "[", RowBox[List["k_", ",", "z_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29