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 Tanh

 http://functions.wolfram.com/01.21.16.0066.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02