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 Tanh

 http://functions.wolfram.com/01.21.16.0082.01

 Input Form

 Tanh[a ArcCosh[z]] == 1 - 2/(1 + (z + Sqrt[-1 + z] Sqrt[1 + z])^(2 a))

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02