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 ArcTanh

 http://functions.wolfram.com/01.27.27.1954.01

 Input Form

 ArcTanh[z] == ((2 Sqrt[z^2])/z) ArcSinh[Sqrt[(1 - Sqrt[1 - z^2])/(2 Sqrt[1 - z^2])]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", SqrtBox[SuperscriptBox["z", "2"]]]], "z"], RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]], "]"]]]]]]]]

 MathML Form

 tanh - 1 ( z ) 2 z 2 z sinh - 1 ( 1 - 1 - z 2 2 1 - z 2 ) z 2 z 2 1 2 z -1 1 -1 1 -1 z 2 1 2 2 1 -1 z 2 1 2 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["ArcSinh", "[", SqrtBox[FractionBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]], "]"]]]], "z"]]]]]

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

 2003-08-21