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 ArcTanh

 http://functions.wolfram.com/01.27.27.0161.01

 Input Form

 ArcTanh[Sqrt[z]] == 2 I ArcSin[Sqrt[(Sqrt[1 - z] - 1)/(2 Sqrt[1 - z])]] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List["2", "\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List["2", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

 tanh - 1 ( z ) 2 sin - 1 ( 1 - z - 1 2 1 - z ) /; 0 < arg ( z ) π Condition z 1 2 2 1 -1 z 1 2 -1 2 1 -1 z 1 2 -1 1 2 Inequality 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], "]"]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

 2003-08-21