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 ArcTanh

 http://functions.wolfram.com/01.27.27.3491.01

 Input Form

 ArcTanh[z] == (-(1/2)) ArcSinh[(2 z)/(z^2 - 1)] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

 tanh - 1 ( z ) - 1 2 sinh - 1 ( 2 z z 2 - 1 ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition z -1 1 2 2 z z 2 -1 -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2007-05-02