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 Tanh

 http://functions.wolfram.com/01.21.16.0067.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02