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 ArcTanh

 http://functions.wolfram.com/01.27.27.0512.01

 Input Form

 ArcTanh[Sqrt[z]] == I ArcCos[1/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["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["1", 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