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 PolyLog

 http://functions.wolfram.com/10.08.21.0020.01

 Input Form

 Integrate[PolyLog[2, (-z) Tan[t]^2], {t, 0, Infinity}] == 2 Pi PolyLog[2, -Sqrt[z]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", InterpretationBox[FractionBox["\[Pi]", "2"], DirectedInfinity[1]]], RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "z"]], " ", SuperscriptBox[RowBox[List["Tan", "[", "t", "]"]], "2"]]]]], "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List["2", "\[Pi]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", " ", SqrtBox["z"]]]]], "]"]]]]]]]]

 MathML Form

 0 Li PolyLog 2 ( - z tan 2 ( t ) ) t 2 π Li PolyLog 2 ( - z ) t 0 DirectedInfinity 1 PolyLog 2 -1 z t 2 2 PolyLog 2 -1 z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "z_"]], " ", SuperscriptBox[RowBox[List["Tan", "[", "t_", "]"]], "2"]]]]], "]"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SqrtBox["z"]]]]], "]"]]]]]]]]

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

 2001-10-29

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