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 ArcTanh

 http://functions.wolfram.com/01.27.27.1642.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21