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 PolyLog

 http://functions.wolfram.com/10.08.03.0032.01

 Input Form

 PolyLog[3, E^(-((2 Pi I)/3))] == (-(4/9)) Zeta[3] - (2 I Pi^3)/81

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["3", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "3"]]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["4", "9"]]], " ", RowBox[List["Zeta", "[", "3", "]"]]]], "-", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "3"]]], "81"]]]]]]]

 MathML Form

 Li PolyLog 3 ( - 2 π 3 ) - 4 9 ζ ( 3 TagBox["3", Rule[Editable, True]] ) - 2 π 3 81 PolyLog 3 -1 2 3 -1 -1 4 9 Zeta Rule Editable 3 -1 2 3 81 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["3", ",", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "9"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", RowBox[List["Zeta", "[", "3", "]"]]]], "-", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", "3"]]], "81"]]]]]]]

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

 2001-10-29