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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.07.17.0017.01









  


  








Input Form





PolyLog[2, z] - PolyLog[2, -z] + PolyLog[2, (1 - z)/(1 + z)] - PolyLog[2, -((1 - z)/(1 + z))] == Pi^2/4 + Log[z] Log[(1 + z)/(1 - z)] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z] && !IntervalMemberQ[Interval[{1, Infinity}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", "z"]]]], "]"]], "+", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]]]], "]"]], "-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", FractionBox[RowBox[List["1", "-", "z"]], RowBox[List["1", "+", "z"]]]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "+", RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["1", "-", "z"]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]]]]]]








MathML Form







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Rule Form





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





2001-10-29