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 Coth

 http://functions.wolfram.com/01.22.16.0066.01

 Input Form

 Coth[ArcCos[z]] == 1 + 2/(-1 + E^Pi (I z + Sqrt[1 - z^2])^(2 I))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", RowBox[List["ArcCos", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["1", "+", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], ")"]], RowBox[List["2", " ", "\[ImaginaryI]"]]]]]]]]]]]]]]

 MathML Form

 coth ( cos - 1 ( z ) ) 1 + 2 π ( z + 1 - z 2 ) 2 - 1 z 1 2 z 1 -1 z 2 1 2 2 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["ArcCos", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", "\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], ")"]], RowBox[List["2", " ", "\[ImaginaryI]"]]]]]]]]]]]]]]

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

 2007-05-02