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 Tanh

 http://functions.wolfram.com/01.21.16.0090.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02