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 Tanh

 http://functions.wolfram.com/01.21.16.0085.01

 Input Form

 Tanh[I ArcCoth[z]] == -1 + 2/(1 + (1 - 1/z)^I/(1 + 1/z)^I)

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02