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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[2,z] > Specific values > Values at fixed points





http://functions.wolfram.com/10.07.03.0015.01









  


  








Input Form





PolyLog[2, (Sqrt[5] - 1)/2] == Pi^2/10 - Log[(Sqrt[5] - 1)/2]^2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List[SqrtBox["5"], "-", "1"]], "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "10"], "-", SuperscriptBox[RowBox[List["Log", "[", FractionBox[RowBox[List[SqrtBox["5"], "-", "1"]], "2"], "]"]], "2"]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mn> 10 </mn> </mfrac> <mo> - </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 10 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ln /> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "-", "1"]], ")"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "10"], "-", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SqrtBox["5"], "-", "1"]], ")"]]]], "]"]], "2"]]]]]]]


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





2001-10-29