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 Tanh

 http://functions.wolfram.com/01.21.16.0084.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02