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 Tanh

 http://functions.wolfram.com/01.21.16.0068.01

 Input Form

 Tanh[ArcTan[x, y]] == -1 + 2/(1 + ((x + I y)/Sqrt[x^2 + y^2])^(2 I))

 Standard Form

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

 MathML Form

 tanh ( tan - 1 ( x , y ) ) 2 ( x + y x 2 + y 2 ) 2 + 1 - 1 x y 2 x y x 2 y 2 1 2 -1 2 1 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tanh", "[", RowBox[List["ArcTan", "[", RowBox[List["x_", ",", "y_"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "1"]], "+", FractionBox["2", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], SqrtBox[RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]], ")"]], RowBox[List["2", " ", "\[ImaginaryI]"]]]]]]]]]]]]

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

 2007-05-02