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 Coth

 http://functions.wolfram.com/01.22.16.0084.01

 Input Form

 Coth[I ArcTanh[z]] == 1 + 2/(-1 + (1 + z)^I/(1 - z)^I)

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02