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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[2,z] > Identities > Functional identities > Involving three dilogarithms





http://functions.wolfram.com/10.07.17.0015.01









  


  








Input Form





PolyLog[2, z^2] - 2 (PolyLog[2, -z] + PolyLog[2, z]) == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["z", "2"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", "z"]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]]]], ")"]]]]]], "\[Equal]", "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> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["z_", "2"]]], "]"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", "z_"]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]]]], ")"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]


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





2001-10-29